Answer Key
Question 1 (Worth 1 points)
(03.03 MC)
The annual growth of Noah's worm collection is represented by the table. What does the f(x) = 4 represent?
x 0 2 4
f(x) 4 16 64
The number of new worms each year
The number of worms Noah started with
The common ratio of worm growth
The average rate of change of worm growth each year
Points earned on this question: 1
Question 2 (Worth 1 points)
(03.03 MC)
A talent competition on television had five elimination rounds. After each elimination, only one-third of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:
x 1 2 3 4 5
f(x) 243 81 27 9 3
Compute the average rate of change of f(x) from x = 1 to x = 4, and describe what it represents.
−78 contestants per round, and it represents the number of contestants who will reach the final round
−234 contestants per round, and it represents the number of contestants who will reach the final round
−234 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
−78 contestants per round, and it represents the average rate at which the number of contestants changed from the first round to the fourth round
Points earned on this question: 1
Question 3 (Worth 1 points)
(03.03 MC)
The table represents a continuous exponential function f(x).
x 2 3 4 5
f(x) 9 3 1 one-third
Graph f(x) and identify the y-intercept.
9
15
36
81
Points earned on this question: 0
Question 4 (Worth 1 points)
(03.03 MC)
Terrance invested money in a technology stock whose growth is modeled by the function f(x) = 0.01(2)x, where x represents number of days. Find the approximate average rate of change from day 3 to day 8.
0.496
2.016
2.48
5
Points earned on this question: 1
Question 5 (Worth 1 points)
(03.03 MC)
Does the function f of x equals 4 times the quantity 1 over 3 end quantity to the x power represent growth or decay? What is the y-intercept of f(x)?
Growth; (0, 4)
Growth; 0 comma one-third
Decay; (0, 4)
Decay; 0 comma one-third
Points earned on this question: 1
Question 6 (Worth 1 points)
(03.03 LC)
Which of the following options results in a graph that shows exponential decay?
f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x
Points earned on this question: 1
Question 7 (Worth 1 points)
(03.03 LC)
The number of members, f(x), in Joe's health club increased by 25% every year over a period of x years. The function below shows the relationship between f(x) and x:
f(x) = 15(1.25)x
Which of the following graphs best represents the function?
graph of exponential function going up from left to right through the point 0 comma 1 and approximately 6 tenths comma 6
graph of exponential function going up from left to right through the point 0 comma 15 and approximately 5 comma 45
graph of exponential function going up from left to right in quadrant 1 through the point 0, 0 and continuing toward infinity
graph of exponential function going up from left to right through the point 0 comma 1 and approximately 4 comma 3
Points earned on this question: 1
Question 8 (Worth 1 points)
(03.03 MC)
A bacteria is growing by a factor of 2 every hour from 1 p.m. to 11 p.m. The function below shows the number of bacterial cells, f(x), after x hours from 1 p.m.:
f(x) = 20(2)x
Which of the following is a reasonable domain for the function?
All positive integers
1 ≤ x ≤ 11
0 ≤ x ≤ 20
0 ≤ x ≤ 10
Points earned on this question: 0
Question 9 (Worth 1 points)
(03.03 MC)
Enrollment at a golf academy has grown exponentially since the academy opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 4.
An exponential graph has time in years on the x axis and enrollments on the y axis. An upward rising curve begins at zero comma fifteen and passes through four comma seventy five.
0.067
4
15
75
Points earned on this question: 1
Question 10 (Worth 1 points)
(03.03 MC)
The number of subscribers, f(t), to a newspaper after t years is shown by the equation below:
f(t) = 75(0.95)t
Which conclusion is correct about the number of subscribers to the newspaper?
It increased by 75% every year.
It decreased by 75% every year.
It increased by 5% every year.
It decreased by 5% every year.
Points earned on this question: 1
