**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Graph the function.**

1) f(x) = (1/4)^{x}

A)

B)

C)

D)

2) f(x) = 5(x – 2 ) – 2

A)

B)

C)

D)

3) f(x) = 2^{-x} – 2

A)

B)

C)

D)

4) f(x) = (0.6)^{x}

A)

B)

C)

D)

5) f(x) = 5^{x}

A)

B)

C)

D)

**Solve the equation.**

6) Solve for x: 3(1 + 2x) = 27

A) 9

B) -1

C) 1

D) 3

7) Solve for x: 2^{4x} = 8^{(x + 5)}

A) -5

B) 5

C) -15

D) 15

8) Solve for x: (ex)^{x} ⋅ e^{27} = e^{12X}

A) {9}

B) {-3, -9}

C) {3, 9}

D) {3}

9) Solve for t: e^{-0.07t} = 0.05 Round your answer to four decimal places.

A) -66.4815

B) -70.1312

C) 44.321

D) 42.7962

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

**Solve the problem.**

10) In the table below, the amount of the U.S. minimum wage is listed for selected years.

U.S Minimum Wage

Year |
1661 |
1967 |
1974 |
1980 |
1981 |
1990 |
1991 |
1996 |
1997 |

Wage |
$1.15 |
$1.40 |
$2.00 |
0 |
$3.35 |
$3.80 |
$4.25 |
$4.75 |
$5.15 |

Find an exponential regression model of the form y = a ⋅ b^{x}, where y represents the U.S. minimum wage x years after 1960. Round a and b to four decimal places. According to this model, what will the minimum wage be in 2005? In 2010?

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

11) Hi-Tech UnWater begins a cable TV advertising campaign in Miami to market a new water. The percentage of the target market that buys water is estimated by the function w(t) = 100(1 – e^{-0.02t}) t represents the number of days of the campaign. After how long will 90% of the target market have bought the water?

A) 120 days

B) 115 days

C) 3 days

D) 90 days

12) The number of books in a community college library increases according to the function B = 7200e^{0.03t}

where t is measured in years. How many books will the library have after 8 year(s)?

A) 10,275

B) 9153

C) 7200

D) 4462

13) Since life expectancy has increased in the last century, the number of Alzheimer’s patients has increased dramatically. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled by the exponential function y = 4.19549⋅(1.02531)^{x} where x is the years since 2000. Estimate the Alzheimer’s patients in 2025. Round to the nearest tenth.

A) 3.9 million

B) 8.0 million

C) 7.8 million

D) 4.8 million

14) A sample of 800 grams of radioactive substance decays according to the function A(t) = 800e^{-0.028t} where t is the time in years. How much of the substance will be left in the sample after 10 years? Round to the nearest whole gram.

A) 605 grams

B) 9 grams

C) 800 grams

D) 1 gram

15) The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function R(t) = 207 e^{0.005t} where t is the number of years since 1960. Estimate the of cases in the year 2010.

A) 266

B) 190

C) 207

D) 240

16) An initial investment of $12,000 is invested for 2 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period.

A) $12,994.28

B) $12,979.20

C) $994.28

D) $12,865.62

17) Suppose that $2200 is invested at 3% interest, compounded semiannually. Find the function for the amount of money after t years.

A) A = 2200 (1.015)^{t}

B) A = 2200 (1.015)^{2t}

C) A = 2200 (1.03)^{2t}

D) A = 2200 (1.0125)^{2t}

**Use the REGRESSION feature on a graphing calculator.**

18) A strain of E-coli Beu-recA441 is placed into a petri dish at 30 Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured.

Time in hours, x |
Population, y |

0 |
0 |

2.5 |
0.18 |

3.5 |
0.26 |

4.5 |
0.35 |

6 |
0.50 |

Find the exponential equation in the form y = a ⋅ b^{x}, where x is the hours of growth. Round to four decimal places.

A) y = 0.0903^{x}

B) y = 1.3384 ⋅ 0.0903^{x}

C) y = 0.0903 ⋅ 1.3384^{x}

D) y = 1.3384^{x}

19) The total cost of the Democratic and the Republican national conventions has increased 596% over the 20-year period between 1980 and 2004. The following table lists the total cost, in millions of dollars, for selected years.

Year, x |
Cost, y |

1980, = 0 |
$23.1 |

1984, x = 4 |
31.8 |

1988, x = 8 |
44.4 |

1992, x = 2 |
58.8 |

1996, x = 6 |
90.6 |

2000, x = 20 |
160.8 |

2004, x = 24 |
170.5 |

Find the exponential functions that best estimates this data. Round your answer to four decimal places

A) y = 1.0929 ⋅ (22.2887)^{x}

B) y = 22.2887x ⋅ (1.0929)^{x}

C) y = 6.6643x + 2.8857

D) y = 22.2887 ⋅ (1.0929)^{x}

**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

20) A particular bacterium is found to have a doubling time of 20 minutes. If a laboratory culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how many bacteria will be present in 55 minutes? Use six decimal places in the interim calculation for the growth rate.

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