Quiz about Exponential Growth and Decay

Question 1

Which inequality best represents the domain of the part shown?

Accepted Answer

$$x>-2$$

Answer

$$x>1$$

Answer

$$y>1$$

Answer

$$y>-2$$

Question 2

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 3

Based on the table, which function represents the same relationship?

Accepted Answer

$$q\left(x\right)=0.0625\left(4\right)^x$$

Answer

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

Answer

$$q\left(x\right)=256\left(0.25\right)^x$$

Answer

$$q\left(x\right)=0.5\left(4\right)^x$$

Question 4

Which graph best represents $$y=10\left(0.85\right)^x$$ ?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 5

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 6

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.

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 7

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

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 8

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 9

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 10

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 11

The starting annual salary for an office worker at a company is $29,000. If the company awards an annual increase of 6.2%, which graph models this situation after the office worker receives $$x$$ annual increases?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Exponential Growth and Decay

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