The estimated value of cos(48) by using tangent line is found to be
0.99989.
Explain about the tangent line ?A straight line which thus touches a function only once is called a tangent line.
The first step is to calculate y when x=π/4. We will receive that target coordinate point as a result.
The required coordinate point is ( π/ 4, √(2) / 2)
The derivative of such function y is then discovered.
y ' = -sin(x)
Input the derivative with the value of x. This corresponds to the tangent line's slope.
y' = -sin(π/4)
y' = - √(2) / 2
The slope plus coordinate point are now entered into the gradient intercept form of the formula to obtain b.
y = mx + b
√(2) / 2 = (-√(2) / 2)(π / 4) + b
√(2) / 2 = (-π√(2) / 8) + b
(√(2) / 2) + (π√(2) / 8) = b
[4√(2) + π√(2)] / 8 = b
[(4 + π)√(2)] / 8 = b
The tangent line comes out to be:
y = (-√(2) / 2)x + [(4 + π)√(2) / 8]
Now , for cos(48).
48° = π/180 * 48 radians
48° = 3.14/180 * 48 radians
48° = 0.01744*48 radians
48° = 0.83712 radians
So, cos(48) = cos( 0.83712 )
Using scientific calculator:
cos(48) = cos( 0.83712 ) = 0.99989
Thus, the estimated value of cos(48) by using tangent line is found to be
0.99989.
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Suppose you start with a full tank of gas (14 gallons) in your truck. After driving 5 hours, you now have 5 gallons left. If x is the number of hours you have been driving, then y is the number of gallons left in the tank. At what rate is the gas left in the tank changing? State your answer as a reduced fraction.
Answer:
We can use the formula for average rate of change to find the rate at which the gas is being used:
average rate of change = (change in y) / (change in x)
where y is the number of gallons left in the tank and x is the number of hours driven.
Substituting the given values, we get:
average rate of change = (5 - 14) / (5 - 0)
Simplifying, we get:
average rate of change = -9/5
Therefore, the rate at which the gas is being used is -9/5 gallons per hour, or -1.8 gallons per hour. This means that the gas in the tank is decreasing at a rate of 1.8 gallons per hour.
In 2021, Madison Square Garden employed 8,900 people. For a basketball game at the garden, there are seats for 19,812 fans. What is the number of fans per employee during a basketball game? Round to the nearest tenth.
Answer:
There are 2.2 fans per employee.
Step-by-step explanation:
19812/8900 = 2.2 Rounded.
Helping in the name of Jesus.
Please helpppppppp!!!!
The 3rd graph is the correct one representing the open sentence.
What is an Inequality?Inequalities is defined as the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values or data. The equal sign in between can be replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
-5≤n-2≤2
First you need to get n by itself, so add 2 to all 3 terms:
-5 +2 ≤ n-2+2 ≤ 2+2
Simplify:
-3 ≤ n ≤ 4
The less than or equal to signs (≤) mean the dots on the line graph are solid.
And n is between -3 and positive 4, the 3rd graph is the correct one.
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For problems 6 and 7 set up a proportion and solve.
i’ll give brainlist
Answer:
Step-by-step explanation:
Number 6 is 50,432
Number 7 is 567654
14 yd
21 yd find the area of the triangle
Answer:
147
Step-by-step explanation:
A= h^b b=21*14= 147
Answer the question below
Answer:
Step-by-step explanation:
This question's answer is 'c'. In the first function here we put the value of x=0, then y =3 but in the second function if we put the value of x=0 then y =2. so c is the correct answer.
What are the steps to solving the following problem,
5x+4=19
List at least 4 steps
Answer:
5x+4=19
5x=19-4
5x=15
5x÷5=15÷5
x=3
Increase the number 15/16 by 3/5 of it of it. Then increase the resulting number by 3/5 of it
The resulting number is 12/5
What are arithmetical operations?Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.
Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it
So, performing the operations,
15/16+15/16×3/5
= 15/16(1+3/5)
= 15/16(8/5)
= 120/80
= 3/2
Now,
3/2+3/2×3/5
= 3/2(1+3/5)
= 3/2(8/5)
= 24/10
= 12/5
Hence, the resulting number is 12/5
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Help woth math problems
The standard form of the quadratic functions can be analyzed, by finding the specified coordinates as follows;
1. Vertex; (2, -3)
Axis of symmetry; x = 2
Minimum value; -3
Range; y ≥ -3
2. Vertex; (1, 4)
Axis of symmetry; x = 1
Maximum value; 4
Range; y ≤ 4
3. Vertex; (-3, -1)
Axis of symmetry; x = -3
Maximum value; -1
Range; y ≤ -1
4. Vertex; (-3, 5)
Axis of symmetry; x = -3
Maximum value; 5
Range; y ≤ 5
5. Vertex; (-0.75. -6.125)
Axis of symmetry; x = -0.75
Minimum value; -6.125
Range; y ≥ -6.125
6. Vertex; (2/3, 4/3)
Axis of symmetry; x = 2/3
Maximum value; 4/3
Range; y ≤ 4/3
Please find attached the graphs for the quadratic equations in question 7, 8, 9 and 10, created with MS Excel.What is the standard form of a quadratic function?The standard form of a quadratic function is the form; f(x) = a·x² + b·x + c, a, b, and c are constants and a ≠ 0.
1. The x-value of the vertex point of the quadratic equation; y = ax² + bx + c is; x = -b/(2·a)
Therefore, the x-value of the vertex point of the equation, y = x² - 4·x + 1 is; x = 4/2 = 2
The y-value of the vertex point is; y = 2² - 4×(2) + 1 = -3
The vertex is; (2, -3)
The axis of symmetry if the x-value of the vertex point, therefore;
The axis of symmetry is; x = 2
The minimum value is the y-value of the vertex point, therefore;
The minimum value is; y = -3
The range is the set of the possible y-values
The positive leading coefficient of the function, indicates that the range of the function is the set of values larger than the minimum value.
Therefore, the range is; y ≥ -3
2. The x-value of the vertex point of the equation, y = -x² + 2·x + 3, therefore is; x = -2/(-2) = 1
The y-value at the vertex point is; y = -1² + 2×1 + 3 = 4
The vertex is; (1, 4)
The axis of symmetry is; x = 1
The maximum value is; y = 4
The range is; y ≤ 4
3. The x-value of the vertex is; x = -(-6)/(2 × (-1)) = -3
The y-value at the vertex is; y = -(-3)² × -6 × (-3) - 10 = -1
The vertex is; (-3, -1)
The axis of symmetry is; x = -3
The maximum value is; y = -1
The range is; y ≤ -1
4. The x-value of the vertex is; x = -18/(2×3) = -3
The y-value of the vertex is; y = 3 × (-3)² + 18 × (-3) + 32 = 5
The vertex is; (-3, 5)
The axis of symmetry is; x = -3
The minimum value is; y = 5
The range is; y ≥ 5
5. The x-value of the vertex is; x = -3/(2 × 2) = -3/4
The y-value of the vertex is; y = 2 × (-3/4)² + 3 × (-3/4) - 5 = -6.125
The vertex is; (-3/4, -6.125)
The axis of symmetry is; x = -3/4
The minimum value is; -6.125
The range is; y ≤ -6.125
6. The x-value of the vertex is; -4/(2 × (-3)) = 2/3
Y-value at the vertex is; y = -3 × (2/3)² + 4 × (2/3) = 4/3
The vertex point is; (2/3, 4/3)
The axis of symmetry is; x = 2/3
The maximum value is; 4/3
The range is; y ≤ 4/3
7. The graphs of the quadratic equations can be obtained by finding the coordinates of the vertex, the y-intercept and the x-intercepts and joining the points using a curve symmetrical about the vertex as follows;
The following values are obtained using an online tool.
7. The graph of the equation; y = x² + 2·x - 5, can be obtained using the following points;
The vertex is; (-1, -4)
The y-intercept is; (0, -5)
The x-intercepts are; (-1 + √6, 0), and (-1 - √6, 0)
8. The graph of the equation; y = -x² + 3·x + 1, can be obtained using the following points;
The vertex is; (3/2, 5/4)
The y-intercept is; (0, 1)
The x-intercepts are; (-0.30, 0), and (3.30, 0)
9. The graph of the equation; y = 2·x² + 4·x - 4, can be obtained using the following points;
The vertex is; (-1, -6)
The y-intercept is; (0, -4)
The x-intercepts are; (-1 + √3, 0), and (-1 - √3, 0)
10. The graph of the equation; y = (-1/2)·x² - 3·x + 3, can be obtained using the following points;
The vertex is; (-3, 7.5)
The y-intercept is; (0, 3)
The x-intercepts are; (-3 + √(15), 0), and (-1 - √(15), 0)
Please find attached the graphs of the quadratic equations created with MS Excel
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Which of the following equation will produce the graph shown below
The quadratic equation in the given graph can be written in the vertex-form as:
y = -2(x - 1)² + 4
Which of the equations produce the given graph?We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:
y = a*(x - h)² + k
in the graph we can see that the vertex is (1, 4), replacing that we will get:
y = a*(x - 1)² + 4
In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:
2 = a*(0 - 1)² + 4
2 = a + 4
-2 = a
Then the quadratic is:
y = -2(x - 1)² + 4
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#9. Please help step by step.
The area of the track is closely 1017.36 square feet.
How do we calculate?
The rectangle has dimensions of 84 ft by 36 ft,
we then find the area by:
Area of rectangle = length x width = 84 ft x 36 ft = 3,024 square feet
A_semicircle = (1/2)πr^2 = (1/2) x 3.14 x 18^2 = 508.68 square feet
The total area of the two semicircles is:
2 x A_semicircle = 2 x 508.68 = 1017.36 square feet
The area of the rectangle plus the area of the two semicircles is:
A_track_outer = A_rectangle + 2 x A_semicircle
= 3024 + 1017.36
= 4041.36 square feet
The area of the rectangle (the field) is:
A_field = length x width = 84 ft x 36 ft = 3024 square feet
We will subtract the area of the field from the area of the track to find the area of the track itself:
Area of track = A_track_outer - A_field
= 4041.36 - 3024
= 1017.36 square feet
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Find the mean of the following data : Marks 0-10 No. of students 5 0-20 10 0-30 14 0-40 17 Ans/22 0-50 20
Mean of the data as per the increasing intervals data is 17.80.
Define mean?The mean in statistics is calculated by multiplying all the values in a set of data by the total number of values for a given set of observations. To put it another way, all that is necessary to determine the mean of a set of data is to sum up all the values and divide the total by the number of values.
Now in the given table,
The midpoints of the intervals are as follows:
0+10/2 = 5
0+20/2 = 10
0+30 /2 = 15
0+40/2 = 20
0+50/2 = 25.
Now total students × interval midpoints are as follows:
5×5=25
10×10=100
15×14=210
20×17=340
25×20=500
Now, total no of students is = 5+10+14+17+20 = 66
So, mean of the data =
(25+100+210+340+500)/66
= 17.80
Therefore, mean of the data is 17.80.
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In 1846 the depth of the river was 6.7 feet deep.
In 1847 it dropped 22%.
This year, 1848, it rose 10%.
You get to choose how you want to cross the river.
1. Raft (90% chance of crossing) + 0 bonus points
2. Float (75% chance of crossing) + 100 bonus points
3. Ford (60% chance of crossing) + 250 bonus points
You only get the bonus points if you cross safely.
You will lose supplies if you sink.
Complete the table to find the depth of the river each
year and enter your choice: 1, 2, or 3.
Year
1846
1847
1848
Choice?
Percent (%)
Change
-22
+10
Submit River Depth
Depth
6.7
Answer:
Step-by-step explanation:
A population is normally distributed with a mean of 56 and a standard deviation of 12.
What is the mean of the sampling distribution for this population?
The calculated value mean of the sampling distribution for this population is 56
Calculating the mean of the sampling distribution for this population?The mean of the sampling distribution for a population with a normal distribution is equal to the population mean.
Therefore, in this case, the mean of the sampling distribution is also 56.
To understand why this is the case, we can consider the central limit theorem, which states that the sampling distribution of the mean of a random sample from a population with any distribution will be approximately normal if the sample size is large enough.
This means that as the sample size increases, the mean of the sampling distribution approaches the population mean.
Therefore, the mean of the sampling distribution for this population is 56.
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Are the fractions 2/2 and 8/8 equivalent fractions
Answer:
Step-by-step explanation:
yes since they are both divisible by their denominators and equal the same thing
Answer:
yes, they are equivalent
Step-by-step explanation:
2/2 = (2/2)x(4/4) = 8/8 = 1
Tom recorded the outdoor temperature for 8 consecutive days. Seven of those temperatures were 71, 80, 69, 80, 73, 77, and 70. The average for all 8 days was 75. What was the temperature on the eighth day?
Answer:
The temperature on the eighth day is 80.
Step-by-step explanation:
Let t = temperature on the eighth day.
[tex] \frac{71 + 80 + 69 + 80 + 73 +77+ 70 + t}{8} = 75[/tex]
[tex] \frac{520 + t}{8} = 75[/tex]
[tex]520 + t = 600[/tex]
[tex]t = 80[/tex]
There are bags of rice in 2850kg. if a bag weighs 50kg, find the value
Answer:
To find the number of bags of rice in 2850kg, we need to divide the total weight of rice by the weight of each bag. In this case, each bag weighs 50kg, so:
Number of bags = 2850 kg / 50 kg per bag
Simplifying this expression, we get:
Number of bags = 57 bags
Therefore, there are 57 bags of rice in 2850kg.
To find the value, we need to know the price per bag of rice. If we know this price, we can simply multiply the number of bags by the price per bag to get the total value. Without knowing the price, we cannot determine the value.
Answer:
57
Step-by-step explanation:
p=6t. what is the value of p when t= 14
Answer:
p=84
Step-by-step explanation:
p=6×14
p=84
answer: p=84
Which equation can be used to find A, the area of the parallelogram shown? A = 5 × 9 A = 4 × 9 A = 12 × 5 × 9 A = 12 × 4 × 9
Which equation can be used to find A, the area - 1
The area of the parallelogram can be found out by using the equation:
A = 4 × 9 = 36m².
Define area of parallelogram?By multiplying the base with the altitude, one can determine the area of a parallelogram. A parallelogram's base and height are perpendicular to each another.
Area of parallelogram = b × h square units
Now in the question,
Height of parallelogram, h = 4m
base of parallelogram, b = 9m
Area of parallelogram = b × h
= 4 × 9
=36m²
Therefore, the equation A = 4 × 9 can be used to find the area of the parallelogram.
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F(x)=x 2 what is f(2)
we input the value 2 into the function, it will output the value 4.
What is Function?Each element of X is given precisely one element of Y by the function from a set X to a set Y. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively. Initially, functions represented the idealized relationship between two variable quantities.
The function F(x) = x^2 represents a quadratic function, where the input value (x) is squared to produce the output value (F(x)).
To find the value of F(2), we simply need to substitute 2 in place of x in the equation:
F(2) = (2)^2 = 4
This means that when we input the value 2 into the function, it will output the value 4.
In other words, F(2) represents the value of the quadratic function at the point where x is equal to 2.
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Complete question:
If F(x)=x^2 then what is f(2).
A rubber bouncy ball is dropped from a
height of 187.00 cm onto a hard flat floor.
After each bounce, the ball returns to a
height that is 3/4 of the previous
maximum height. What is the maximum
height reached after the 13th bounce?
The maximum height reached after the 13th bοunce is 6.14 cm.
What is height οf bοunce?The height οf bοunce is the height tο which an οbject rebοunds after cοIIiding with a surface, such as a baII bοuncing οn the grοund οr a diver bοuncing οff a diving bοard. The height οf the bοunce depends οn severaI factοrs, incIuding the initiaI height οf the οbject, the surface it cοIIides with, the eIasticity οf the οbject and the surface, and the angIe οf incidence.
Tο sοIve this prοbIem, we need tο use the fοrmuIa fοr the height οf each bοunce:
[tex]h = (3/4)^{{n}} \times H[/tex]
where h is the height οf the nth bοunce, H is the initiaI height (in this case, 187.00 cm), and n is the number οf bοunces.
We want tο find the maximum height reached after the 13th bοunce, which means we need tο find the height οf the 13th bοunce and then muItipIy it by 3/4 tο get the maximum height.
Using the fοrmuIa abοve, we can find the height οf the 13th bοunce:
[tex]h = (3/4)^{{13}} \times 187.00[/tex]
h ≈ 8.18 cm
Nοw we can find the maximum height:
maximum height = (3/4) × h
maximum height = (3/4) ×8.18
maximum height ≈ 6.14 cm
Therefοre, the maximum height reached after the 13th bοunce is apprοximateIy 6.14 cm.
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The Revenue and Cost equations for a company are known to be polynomials of order 1 and 2 respectively. It is also known that the graphs of the two equations meet at points A(1,1) and B(5,9) while the third point of the cost function is C(2,0), obtain the following:
a) The Revenue equation and the cost equation
b) What do the common solutions to the two equations signify?
Answer: a) We know that the Revenue equation is a polynomial of order 1, so we can write it in the form:
R(x) = ax + b
where a and b are constants to be determined. We also know that R(1) = 1 and R(5) = 9, so we have two equations:
a(1) + b = 1
a(5) + b = 9
Solving these equations simultaneously, we get:
a = 2, b = -1
Therefore, the Revenue equation is:
R(x) = 2x - 1
Similarly, the Cost equation is a polynomial of order 2, so we can write it in the form:
C(x) = ax^2 + bx + c
where a, b, and c are constants to be determined. We know that C(1) = R(1) = 1 and C(5) = R(5) = 9, so we have two equations:
a(1)^2 + b(1) + c = 1
a(5)^2 + b(5) + c = 9
We also know that C(2) = 0, so we have a third equation:
a(2)^2 + b(2) + c = 0
Solving these equations simultaneously, we get:
a = 1, b = -4, c = 4
Therefore, the Cost equation is:
C(x) = x^2 - 4x + 4
b) The common solutions to the Revenue and Cost equations represent the production level(s) at which the company makes a profit, since the Revenue equation represents the amount of money the company earns and the Cost equation represents the amount of money the company spends. In other words, the common solutions are the values of x for which R(x) - C(x) > 0. At these production levels, the company's revenue is greater than its cost, resulting in a profit. At production levels where R(x) - C(x) < 0, the company is making a loss. At production levels where R(x) - C(x) = 0, the company is breaking even. Therefore, the common solutions to the two equations signify the production levels at which the company makes a profit or breaks even.
Step-by-step explanation:
You deposit $3400 in an account with an annual interest of 3.3% for 10 years.
The amount of money you'll have at the end of 10 years is $
(Type an integer or a decimal.)
Answer: 3.3= .033 percentage. .033 times 34000=1112 times (t) time (10 years) equals 11120
Step-by-step explanation:
100 Points!!! Algebra graphing question. Describe the reflection in the function as it relates to the parent graph. Then graph the function. Y=-|x| Photo attached. Thank you!!
The graph of the function y = -|x| is the graph of the function y = |x| reflected across the x-axis
How to describe the graph of the function y = |x|The function given in the question is
y = -|x|
The above function is an absolute value function graph
And the parent function of an absolute graph is
y = |x|
When y = |x| and y = -|x| compared, we have the transformation to be
A reflection across the x-axis
This means that the graph of y = |x| is reflected across the x-axis to create y = -|x|
See attachment for the graph of the function
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A(-4,4) B(2,7) C(2,1) where is the orthocenter
Answer:
Step-by-step explanation:
(1\2, 4) = (0.5, 4)
if mFI = 64 degrees and mRS = 180 degrees, find m
find the non permissible replacement for (x ^ 2 + 1)/(2x + 10)
Reason:
We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,
2x+10 = 0
2x = -10
x = -10/2
x = -5
Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.
I couldn’t solve this and I was very confused, if anyone can please help me on this I will appreciate it, thank you so much
It is due tomorrow
no 1) what is the square root of 2? it's about 1.5
no 2) pi is 3.14 blah blahblah so just put somewhere around 3
no 3) do square root of 11, it's about 3.3 so put it a tiny bit after no 2.
all of these will be after the 0, not before because theyre positive
hope this helps x
A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region bounded by the graph of x^2 + y^2 = 50^2 with x ≥ 0 and y ≥ 0. The following equations are models for the floor and ceiling. Floor: z = x+y/ 5 Ceiling: z = 20 + xy /100 Calculate the volume of the room, which is needed to determine the heating and cooling requirements.
Answer:
Step-by-step explanation:
To calculate the volume of the room, we need to integrate the difference between the ceiling and floor functions over the region bounded by the circle. We can use double integrals to do this.
First, let's rewrite the equations for the floor and ceiling in terms of x and y:
Floor: z = (x + y) / 5
Ceiling: z = 20 + xy / 100
The volume of the room can be calculated using the following double integral:
V = ∫∫(20 + xy/100 - (x + y)/5) dA
where the limits of integration are x = 0 to x = 50, and y = 0 to y = √(50^2 - x^2).
We can simplify the integrand by combining like terms:
V = ∫∫(400/100 + xy/100 - (20x + 20y)/100) dA
V = ∫∫(4 + xy/100 - 0.2x - 0.2y) dA
Now we can integrate with respect to y first:
V = ∫0^50 ∫0^√(50^2 - x^2) (4 + xy/100 - 0.2x - 0.2y) dy dx
V = ∫0^50 [(4y + xy^2/200 - 0.2xy - 0.1y^2)|y=0^√(50^2 - x^2)] dx
V = ∫0^50 [(4√(50^2 - x^2) + x(50^2 - x^2)/200 - 0.2x√(50^2 - x^2) - 0.1(50^2 - x^2)^2/200)|x=0^50]
Evaluating this integral, we get:
V ≈ 2,233.5 cubic feet
Therefore, the volume of the room is approximately 2,233.5 cubic feet, which is the amount of space that will need to be heated or cooled.
Can someone help me, please
Step by step please
The number of bacteria in a culture is given by the function
n(t)=90e^0.15t
(a) What is the relative rate of growth of this bacterium population?
Your answer is ---------percent
(b) What is the initial population of the culture (at t=0)?
Your answer is---------
(c) How many bacteria will the culture contain at time t=5?
Your answer is----------
(a) The relative rate of growth of the bacterium population is 15% per unit time; (b) the initial population of the culture is 90 bacteria; (c) the culture will contain approximately 239 bacteria at time t=5.
(a) The relative rate of growth of the bacterium population can be calculated by taking the derivative of the function n(t) with respect to t and then dividing it by the value of n(t) at that point, which gives:
relative rate of growth = (dn/dt) / n(t)
= (0.15 * 90[tex]e^0.15t[/tex]) / (90[tex]e^0.15t[/tex])
= 0.15
Therefore, the relative rate of growth is 15%.
(b) The initial population of the culture at t=0 is given by plugging in t=0 in the function n(t):
n(0) = 90[tex]e^0.15[/tex]*0
= 90
Therefore, the initial population of the culture is 90.
(c) The number of bacteria in the culture at time t=5 can be found by plugging in t=5 in the function n(t):
n(5) = 90[tex]e^0.15[/tex]*5
= 385.97 (rounded to two decimal places)
Therefore, the culture will contain approximately 385.97 bacteria at time t=5.
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