Quiz about Exponential Growth & Decay Functions

Question 1

What is the correct function for this problem?

Accepted Answer

$$Y\ =\ 650,000\ \left(1\ +0.04\right)^7$$

Answer

$$Y\ =\ 650,000\ \left(1\ +4\right)^7$$

Answer

$$Y\ =\ 650,000\ \left(1\ -0.4\right)^7$$

Answer

$$Y\ =\ 650,000\ \left(1-0.04\right)^7$$

Question 2

What is the correct function for this problem?

Accepted Answer

$$Y\ =\ 35,000\left(1-0.05\right)^8$$

Answer

$$Y\ =\ 35,000\left(1+0.05\right)^8$$

Answer

$$Y\ =\ 35,000\left(1-5\right)^8$$

Answer

$$Y\ =\ 35,000\left(1-0.5\right)^8$$

Question 3

What does the graph represent?

Accepted Answer

Exponential Decay

Answer

Exponential Growth

Question 4

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

Accepted Answer

y = 15(1.35)^x

Answer

y = 15(35)^x

Answer

y = 15(0.35)^x

Answer

y = 35(1.15)^x

Question 5

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

Accepted Answer

y=6(1.14)^x

Answer

y=6(0.14)^x

Answer

y=6(1+14)^x

Answer

y=6(0.86)^x

Question 6

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

Accepted Answer

y=5000(1 - 0.30)^x

Answer

y=30(5000)^x

Answer

y=5000(1 + 0.30)^x

Answer

Question 7

Write the exponential function for :

A population of beetles that starts at 50 increases by 65% each year.

Accepted Answer

$$f\left(x\right)=\ 50\left(1.65\right)^x$$

Answer

$$f\left(x\right)\ =\ 50\ \left(.65\right)^x$$

Answer

$$f\left(x\right)\ =\ 65\left(.50\right)^x$$

Answer

$$f\left(x\right)=\ 50\left(.35\right)^x$$

Question 8

Write the exponential function for :

Your heart rate reaches 58 bpm and then increases by 20% each minute.

Accepted Answer

$$f\left(x\right)=\ 58\left(1.20\right)^x$$

Answer

$$f\left(x\right)\ =\ 58\ \left(.20\right)^x$$

Answer

$$f\left(x\right)\ =\ 20\left(.58\right)^x$$

Answer

$$f\left(x\right)=\ 58\left(.80\right)^x$$

Question 9

Write the exponential function for :

An account with $25,000 decreases in value 9% each year.

Accepted Answer

$$f\left(x\right)\ =\ 25,000\left(.91\right)^x$$

Answer

$$f\left(x\right)\ =\ 25,000\left(.90\right)^x$$

Answer

$$f\left(x\right)=25,\ 000\left(0.09\right)^x$$

Answer

$$f\left(x\right)=\ 25,000\left(1.09\right)^x$$

Question 10

Alex invests in a savings account that increases by 3.50% quarterly. What is the growth/decay factor?

Accepted Answer

103.50% = 1.035

Answer

1350%= 13.50

Answer

96.5% = .965

Answer

10.35%= .1035

Question 11

To write the exponential function for :

A population of beetles that starts at 50 increases by 65% each year.

What is the 1st step?

Accepted Answer

Add $$100+\ 65\%$$

Answer

Subtract $$100-65\%$$

Answer

change the $$65\ \%$$ to a decimal by moving it two units to the left

Answer

change the $65\ \%$ to a decimal by moving it two units to the righy

Question 12

To write the exponential function for :

An account with $25,000 decreases in value 9% each year.

What is the 1st step?

Accepted Answer

Subtract $$100-9\%$$

Answer

Add $$100+\ 9\%$$

Answer

change the $$9\ \%$$ to a decimal by moving it two units to the left

Answer

change the $$9\%$$ to a decimal by moving it two units to the right

Question 13

Alex invests in a savings account that pays 3.50% interest increases quarterly. What is the decay/growth factor?

Accepted Answer

$$100\ \%\ +\ 3.50\ \%$$

Answer

$$100\%\ -3.50\%$$

Answer

$$100\ \%\ \cdot\ 3.50\ \%$$

Answer

$$100\%\ \div3.50\%$$

Question 14

In an exponential function, to have an increase of 15% you have do the following:

(select 2)

Accepted Answer

$$Add\ \ \ \ \ \ 100\%\ +\ 15\%\ \ \ $$

Accepted Answer

Change 115% to a decimal which is 1.15

Answer

$$Subtract\ \ \ \ 100\%\ -15\%$$

Answer

Change 85% to a decimal which is 0.85

Question 15

In an exponential function, to have an decrease of 9% you have do the following:

(select 2)

Accepted Answer

Change 91% to a decimal which is 0.91

Accepted Answer

$$Subtract\ \ \ \ 100\%\ -9\%$$

Answer

$$Add\ \ \ \ \ \ 100\%\ +\ 9\%\ \ \ $$

Answer

Change 109% to a decimal which is 1.09

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