23 The value of a particular investment follows a pattern of

23) The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 2600e0.063t. When will the account be worth $4584? (Sec. 6.8/Textbook) 23) A) 2011 B) 2008 C) 2010 D) 2009

24) The population of a particular country was 28 million in 1983; in 1997, it was 34 million. The exponential growth function A = 28ekt describes the population of this country t years after 1983. Use the fact that 14 years after 1983 the population increased by 6 million to find k to three decimal places. (Sec. 6.8/Textbook) 24) A) 0.490 B) 0.128 C) 0.024 D) 0.014

25) The half-life of plutonium-234 is 9 hours. If 80 milligrams is present now, how much will be present in 3 days? (Round your answer to three decimal places.) (Sec. 6.8/Textbook) 25) A) 63.495 B) 7.936 C) 45.948 D) 0.312

26) Strontium 90 decays at a constant rate of 2.44% per year. Therefore, the equation for the amount P of strontium 90 after t years is P = P0 e-0.0244t. How long will it take for 15 grams of strontium to decay to 5 grams? Round answer to 2 decimal places. (Sec. 6.8/Textbook) 26) A) 45.03 years. B) 40.50 years C) 450.25 years D) 4.50 years

27) The function A = Aoe-0.01155x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 200 pounds of the material are initially put into the vault, how many pounds will be left after 40 years? (Sec. 6.8/Textbook) 27) A) 71 pounds B) 150 pounds C) 67 pounds D) 126 pounds

28) The logistic growth model P(t) = 1080 1 + 23e-0.346t represents the population of a bacterium in a culture tube after t hours. What was the initial amount of bacteria in the population? (Sec. 6.8/Textbook) 28) A) 44 B) 46 C) 50 D) 45

29) The logistic growth model P(t) = 910 1 + 21.75e-0.351t represents the population of a bacterium in a culture tube after t hours. When will the amount of bacteria be 650? (Sec. 6.8/Textbook) 29) A) 5.69 hours B) 2.12 hours C) 11.38 hours D) 7.82 hours

30) In a town whose population is 3000, a disease creates an epidemic. The number of people, N, infected t days after the disease has begun is given by the function N(t) = 3000 1 + 21.2 e - 0.54t . Find the number of infected people after 10 days. (Sec. 6.8/Textbook) 30) A) 142 people B) 1000 people C) 2737 people D) 2000 people.

Solution

Answers:

25) D

0.312

D) 0.312

after h hours,

80 * (1/2)^(h/9)

That\'s because for every 9 hours, the amount is multiplied by 1/2

so, after 3 days = 24* 3 = 72 hours, we will have

80 * (1/2)^(72/9) = 0.312 mg

30) C

2737 people

N(t)=3000/1+21.2e-0.54t
The -0.54t should be an exponent on e:
N(t)=3000/[1+21.2e^(-0.54t)]
(note the use of grouping symbols which clarify the equation.)
t = 10
N(t)=3000/[1+21.2e^(-0.54(10))] = 2737.846 = 2737people

23) D

2009

26) A

45.03 years.

28) C

50

29) C

11.38 hours