Quiz about Interpreting Exponential Functions 9B/9C

Question 1

The function $$d\left(t\right)=452\left(1.034\right)^t$$ can be used to estimate the number of dingoes in the Australian Outback at the end of t years. What does 1.034 represent in this function?

Accepted Answer

The growth factor of the number of dingoes in the Australian Outback

Answer

The initial number of dingoes in the Australian Outback

Answer

The decay factor of the number of dingoes in the Australian Outback

Answer

The number of dingoes in the Australian Outback at the end of the first year

Question 2

An insect population after x months can be modeled by the function $$g\left(x\right)=18\left(1.3\right)^x$$ . Which statement is the best interpretation of one of the values in this function?

Accepted Answer

The insect population increased at a rate of 30% each month.

Answer

The insect population increased by 13 insects each month.

Answer

The insect population decreased by 13 insects each month.

Answer

The insect population decreased at a rate of 30% each month.

Question 3

A bank account earning annual compound interest was opened, and no additional deposits or withdrawals were made after the initial deposit. The balance in the account after x years can be modeled by $$b\left(x\right)=850\left(1.025\right)^x$$ . Which statement is the best interpretation of one of the values in this function?

Accepted Answer

The balance in the account increases at a rate of 2.5% each year.

Answer

The initial balance of the account decreases at a rate of 97.5% each year.

Answer

The initial balance of the account was $1,025.

Answer

The balance in the account at the end of one year is $850.

Question 4

Scientists are studying a bacteria sample. The function $$f\left(x\right)=245\left(1.12\right)^x$$ gives the number of bacteria in the sample at the end of x days.

Which statement is the best interpretation of one of the values in this function?

Accepted Answer

The number of bacteria increases at a rate of 12% each day.

Accepted Answer

The initial number of bacteria is 245

Answer

The initial number of bacteria is 12.

Answer

The initial number of bacteria decreases at a rate of 88% each day.

Answer

The number of bacteria at the end of one day is 245.

Question 5

A student used $$f\left(x\right)=5.00\left(1.012\right)^x$$ to show how the balance in a savings account will increase over time. What does the 5.00 represent?

Accepted Answer

The starting balance of the savings account

Answer

The interest the savings account earned for the first year

Answer

The annual interest rate of the savings account

Answer

The number of years the savings account has earned interest

Question 6

Researchers studied the population of a town over time and modeled the data using an exponential function.

-The initial estimated population was 12,000

-After the first year, the population of the town was 15,120

If the population of the town continues to grow at this rate each year, which function can be used to model the population x years after the researchers began their study?

Accepted Answer

$$f\left(x\right)=12,000\left(1.26\right)^x$$

Answer

$$f\left(x\right)=12,000\left(0.74\right)^x$$

Answer

$$f\left(x\right)=15,120\left(1.26\right)^x$$

Answer

$$f\left(x\right)=15,120\left(0.74\right)^x$$

Question 7

This year the number of students who participated in sports was 480. Each year the number of students who participate in sports increases by 3%. Which function can be used to model the number of students participating in sports after x years?

Accepted Answer

$$f\left(x\right)=480\left(1.03\right)^x$$

Answer

$$f\left(x\right)=480\left(3\right)^x$$

Answer

$$f\left(x\right)=3x+480$$

Answer

$$f\left(x\right)=1.03x+480$$

Question 8

An exponential function is graphed on the grid. Which function is best represented by the graph?

Accepted Answer

$$p\left(x\right)=\left(0.25\right)^x$$

Answer

$$p\left(x\right)=2\left(0.5\right)^x$$

Answer

$$p\left(x\right)=\left(1.25\right)^x$$

Answer

$$p\left(x\right)=\left(25\right)^x$$

Question 9

Which exponential function models this situation?

HINT: LOOK FOR THE INITIAL VALUE!

Accepted Answer

$$v\left(x\right)=9,000\left(0.9\right)^x$$

Answer

$$v\left(x\right)=9,000\left(1.1\right)^x$$

Answer

$$v\left(x\right)=8,100\left(1.1\right)^x$$

Answer

$$v\left(x\right)=8,100\left(0.9\right)^x$$

Question 10

The graph shows the number of game consoles sold in millions since 2015. Based on this information, which function best models the number of game consoles sold in millions x years since 2015?

Accepted Answer

$$g\left(x\right)=32.7\left(0.58\right)^x$$

Answer

$$g\left(x\right)=0.58\left(32.7\right)^x$$

Answer

$$g\left(x\right)=32.7\left(7.96\right)^x$$

Answer

$$g\left(x\right)=7.96\left(32.7\right)^x$$

Question 11

An exponential function is graphed on the grid.

Accepted Answer

$$g\left(x\right)=6\left(\frac{1}{3}\right)^x$$

Answer

$$g\left(x\right)=6\left(3\right)^x$$

Answer

$$g\left(x\right)=6-\left(\frac{1}{3}\right)^x$$

Answer

$$g\left(x\right)=6-\left(3\right)^x$$

Question 12

There are 1,024 players in a tennis tournament. In each round, half the players are eliminated. Which function can be used to find the number of players remaining in the tournament at the end of x rounds?

Accepted Answer

$$f\left(x\right)=1,024\left(0.50\right)^x$$

Answer

$$f\left(x\right)=1,024\left(1.50\right)^x$$

Answer

$$f\left(x\right)=1,024\left(1.05\right)^x$$

Answer

$$f\left(x\right)=1,024\left(0.05\right)^x$$

Question 13

In the year 1900, the total number of metric tons of copper produced in the world was 495,000. Each year since 1900, the total number of metric tons of copper produced has increased on average by about 3.25% over the amount produced the previous year. Which function models the total number of metric tons of copper produced in the year that is x years since 1900?

Accepted Answer

$$c\left(x\right)=495,000\left(1.0325\right)^x$$

Answer

$$c\left(x\right)=495,000\left(0.9675\right)^x$$

Answer

$$c\left(x\right)=495,000x^{1.0325}$$

Answer

$$c\left(x\right)=495,000x^{0.9675}$$

Question 14

A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 4 of these cells?

Accepted Answer

$$n=4\left(2\right)^h$$

Answer

$$n=4\left(\frac{1}{2}\right)^h$$

Answer

$$n=4+\left(2\right)^h$$

Answer

$$n=4+\left(\frac{1}{2}\right)^h$$

Question 15

The amount of fertilizer in a landscaping company's warehouse decreases at a rate of 3% per week. The amount of fertilizer in the warehouse was originally 78,000 cubic yards. Which function models the amount of fertilizer in cubic yards left after w weeks?

Accepted Answer

$$f\left(w\right)=78,000\left(0.97\right)^w$$

Answer

$$f\left(w\right)=0.97\left(78,000\right)^w$$

Answer

$$f\left(w\right)=1.03\left(78,000\right)^w$$

Answer

$$f\left(w\right)=78,000\left(1.03\right)^w$$

Question 16

A toy is made up of cylindrical rings stacked on a base, as shown in the diagram. The diameter of the base is 5 inches. If the diameter of Ring 1 is 87% of the diameter of the base and each ring after follows the same pattern. Which function can be used to find the diameter in inches of Ring r?

Accepted Answer

$$d\left(r\right)=5\left(0.87\right)^r$$

Answer

$$d\left(r\right)=0.87\left(r-5\right)$$

Answer

$$d\left(r\right)=0.87\left(5\right)^r$$

Answer

$$d\left(r\right)=5\left(r-0.87\right)$$

Interpreting Exponential Functions 9B/9C

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