Free Printable 7.6 - Growth Decay and compounding interest

1.

In March, 2020, before the Covid-19 lockdown, 1,200,000 Texans had applied for unemployment. During the COVID-19 lockdown, the number of people applying for unemployment increased by 4% each month. What exponential function can be used to find the number of people applying for unemployment after x months of COVID-19 lockdown? (a)

Choose from the below words

$y=1,200,000\left(1.04\right)^x$

$y=\ 1,200,000\left(0.04\right)^x$

$y=1,200,000\left(1.4\right)^x$

$y=1,200,000\left(0.06\right)^x$

2.

Which of the following exponential functions represents an initial value of 1780 and a growth of 18% for x years?

(a)

Choose from the below words

$y=1780\left(1.18\right)^x$

$y=1780\left(0.18\right)^x$

$y=\ 1780\ -\ \left(0.18\right)^x$

$y=1780\left(.82\right)$

3.

Chloe was studying earthquake waves in Japan. The function of $f\left(x\right)=354\left(1.15\right)^x$ gives the number of waves at the end of x days. What is the growth rate for this function?

a)

The initial number of waves is 15.

b)

The initial number of waves decreases at a rate of 85% each day.

c)

The initial number of waves increases at a rate of 15% each day.

d)

The number of waves at the end of one day is 354.

4.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

5.

This is an example of:

(a)

Choose from the below words

Exponential Growth

Linear Growth

Linear Decay

Exponential Decay

6.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

7.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much total will she earn in 10 years?

a)

$4915.59

b)

$3933.28

c)

$2979.81

d)

$4005.09

e)

I have no idea

8.

Please label each part of the function with the appropriate descricription.

a)

final value

b)

initial value

c)

growth/decay factor

d)

time

1

2

3

4

1)

2)

3)

4)

9.

What is the benefit of starting to invest early, even with a small amount?

a)

Your investments are likely to grow more since compounding means returns get larger over time

b)

You are guaranteed higher returns since compounding reduces the risks of investing

c)

You can use your investments to meet short-term financial goals since you don't need to hold them as long

d)

You can take advantage of brokerage discounts for long-term investors

10.

You've set a goal of having $12,000 after 18 years. If you estimate that your investment account will have an average yearly growth factor of 1.07, how much money should you invest today? Round to the nearest cent.

(a)

11.

Emilee has $800 to deposit in an investment account that will triple every year. How much money will Emilee have in 4 years?

(a)

12.

Click on the part of the formula that represents the number of compounding periods per year.

A

B

C

D

E

13.

Click on the part of the formula that represents the time in years since the initial investment.

A

B

C

D

E

14.

What does the model P=A(1+r)^t best represent?

a)

Exponential growth

b)

Simple Interest

c)

Compound Interest

d)

Exponential Decay

15.

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

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

16.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

7.6 - Growth Decay and compounding interest

Total questions: 16

Worksheet time: 18mins

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