Exponential Growth Worksheet

**Page 1**

1.

If a quantity increases by the same percent $r$ in each unit of time $t$, then the quantity is ____________.

a. | growing exponentially | ||

b. | decreasing exponentially | ||

c. | constant |

Correct answer : (1)

2.

Which of the following equations represents exponential growth?

a. | $y$ = $r$(1 + $r$) | ||

b. | $y$ = $r$(1 + C) | ||

c. | $y$ = C$r$ | ||

d. | $y$ = C(1 + $r$) ^{$t$} |

Correct answer : (4)

3.

The expression (1 + $r$) is called ______ in the equation $y$ = C(1 + $r$)^{$t$}.

a. | decay factor | ||

b. | growth factor | ||

c. | decay and growth factors | ||

d. | exponent |

Correct answer : (2)

4.

The average length of a person's hair at birth is 0.36 inches. The length of the hair increases by about 10% each day during the first six weeks. Choose a model that represents the average length of the hair during the first six weeks.

a. | $y$ = 0.36(1.1) ^{$t$} | ||

b. | $y$ = -0.36(1.1) ^{$t$} | ||

c. | $y$ = 1.1(0.36) ^{$t$} | ||

d. | None of the above |

[Write exponential growth model.]

= 0.36(1 + 0.10)

[Substitute C = 0.36 and

= 0.36(1.1)

[Add.]

The model for the length of the hair in first six weeks is

Correct answer : (1)

5.

A bank pays 4% interest compounded yearly on a deposit of $900. What will be the balance in the account after 7 years?

a. | $1288 | ||

b. | $1088 | ||

c. | $2376 | ||

d. | $1188 |

= 900(1 + 0.04)

Balance after 7 years

[Substitute P = 900,

= 900(1.04)

[Simplify.]

The account balance after 7 years will be about $1188.

Correct answer : (4)

6.

There are 20 bears in a zoo. What will be their population after 3 years, if the population doubles each year?

a. | 160 bears | ||

b. | 260 bears | ||

c. | 60 bears | ||

d. | 210 bears |

Population after 3 years = 20(2)

[Substitute

= 160

[Simplify.]

There will be 160 bears after 3 years.

Correct answer : (1)

7.

The cost of a movie ticket is $8, which increases by 3% each year. Find the cost of the ticket after 8 years.

a. | $15.00 | ||

b. | $10.00 | ||

c. | $20.00 | ||

d. | $64 |

P = 8 (1 + 0.03)

[Substitute A = 8,

= 8(1.03)

[Simplify.]

The ticket costs about $10.00 after 8 years.

Correct answer : (2)

8.

Rents in a particular area are increasing by 3% every year. Predict what the rent of the apartment would be after 2 years, if its rent is $400 per month now.

a. | $424.36 | ||

b. | $425.36 | ||

c. | $434.36 | ||

d. | $435.36 |

P = 400(1 + 0.03)

[Substitute A = 400,

= 400(1.03)

[Simplify.]

The rent of the apartment after 2 years will be $424.36.

Correct answer : (1)

9.

What is the percent increase in the growth of a tree, if the initial height of the tree is one foot and the height after one year is 1.40 feet?

a. | 30% | ||

b. | 50% | ||

c. | 60% | ||

d. | 40% |

[Exponential growth model.]

From the above equation, the growth factor is given by (1 +

1.40 can be written as (1 + 0.40)

So, the percent increase is 0.40 = 40%

[Compare with the exponential growth equation.]

Correct answer : (4)

10.

The population of the United States was about 250 million in 2003, and is growing exponentially at a rate of about 0.7% per year. What will be its population in the year 2013?

a. | 250 million | ||

b. | 268.1 million | ||

c. | 248.1 million | ||

d. | 230 million |

The percent increase,

The initial population, C = 250 million

[Write exponential growth model.]

= 250(1 + 0.007)

[Substitute C = 250,

= 250(1.007)

[Simplify.]

The population in the year 2013 will be 268.1 million.

Correct answer : (2)