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

Question

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There are currently 59 million cars in a certain country, decreasing by 23% annually. How many years will it take for this country to have 37 million cars? Round to the nearest year.. A) 134 yr B) 20 yr C) 10 yr D) 3 yr SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question 2) Randy invested his inheritance in an account that paid 68% interest, compounded 2) continuously. After 6 years, he found that he now had $52,152.03. What was the original amount of his inheritance? 3) An endangered species of fish has a population that is decreasing exponentially 3) (A - Agekt). The population 10 years ago was 1800. Today, only 900 of the fish are alive. Once the population drops below 100, the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.) 4) A certain radioactive isotope has a half-life of 252 years. Determine the annual decay rate,4) k. 5) Susan purchased a painting in the year 2000 for $3000. Assuming an exponential rate of 5) inflation of 2.1% per year, how much will the painting be worth 5 years later? Solve the equation. 6) log5 (x + 4) = 2 + 10g5 (x-1) 6) Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. 8)

Explanation / Answer

1) current population of cars = 59 million

decreasing by 2.3 % annually

so we can write the function as

P = 59 ( 1 - .023 ) ^t

P = 59 ( 0.977 ) ^t

plugging P = 37

37 = 59 ( 0.977)^t

37/59 = 0.977 ^t

ln ( 37/59 ) = t ln 0.977

t = 20.05

so, it will take 20 years

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