Exponential Functions II Worksheet

**Page 1**

1.

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 1.3 feet?

a. | 50% | ||

b. | 40% | ||

c. | 20% | ||

d. | 30% |

Correct answer : (4)

2.

Rents in a particular area are increasing by 2% every year. Predict the rent of the apartment after 2 years, if its rent is $500 per month now?

a. | $521.2 | ||

b. | $531.2 | ||

c. | $530.2 | ||

d. | $520.2 |

Correct answer : (4)

3.

Which of the following models is an exponential decay model?

a. | $y$ = 10 + 3$t$ | ||

b. | $y$ = $\frac{1}{3}$$t$ ^{2} | ||

c. | $y$ = 8($\frac{3}{7}$) ^{$t$} | ||

d. | $y$ = 12($\frac{4}{3}$) ^{$t$} |

Correct answer : (3)

4.

There are 15 lions in a zoo. What will be their population after 4 years, if the population doubles each year?

a. | 340 lions | ||

b. | 240 lions | ||

c. | 290 lions | ||

d. | 60 lions |

Correct answer : (2)

5.

The price of gold is $300 per 10 grams in the month of January. It loses its value at a rate of 5% per month. Find the cost of the 10 grams gold in the month of August.

a. | $200 | ||

b. | $110 | ||

c. | $210 | ||

d. | $190 |

Correct answer : (3)

6.

A company purchased machinery in the year 1990 for $25,000. Its cost depreciates at a rate of 5% per year. Identify an exponential decay model to represent the cost of the machinery.

a. | $y$ = 25000(0.85) ^{$t$} | ||

b. | $y$ = 25100(0.95) ^{$t$} | ||

c. | $y$ = 25000(0.95) ^{$t$} | ||

d. | $y$ = 24900(0.95) ^{$t$} |

Correct answer : (3)

7.

Frank started a business in the year 1991. He got $27,000 profit in the first year. Each year his profit decreased by 3%. Identify an exponential decay model to represent his decreasing annual profit in the business.

a. | $y$ = 27000(0.87) ^{$t$} | ||

b. | $y$ = 26999(0.97) ^{$t$} | ||

c. | $y$ = 27000(0.97) ^{$t$} | ||

d. | $y$ = 27001(1.07) ^{$t$} |

Correct answer : (3)

8.

The profit made by a software company in 1992 was $448 million. Identify an expression to represent the profit made by the company after $n$ years, if the profit is growing exponentially at a rate of 0.4% per year?

a. | 448(1.004) ^{$n$} | ||

b. | 448(1 - 0.004) ^{$n$} | ||

c. | 448(0.004) ^{$n$} | ||

d. | 448(1 + 1.004) ^{$n$} |

Correct answer : (1)

9.

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(11) ^{$t$} | ||

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

c. | $y$ = 0.36(6$t$) | ||

d. | $y$ = 0.36(0.9) ^{$t$} |

Correct answer : (2)

10.

A bank pays 3% interest compounded yearly on a deposit of $600. What will be the balance in the account after 4 years?

a. | $575 | ||

b. | $1350 | ||

c. | $675 | ||

d. | $775 |

Correct answer : (3)