In 2000, there were about 202 million vehicles and about 279 million people in a

Question

In 2000, there were about 202 million vehicles and about 279 million people in a certain country. The number of vehicles has been growing at 4.5% a year, while the population has been growing at 196 a year. (a) Write a formula for the number of vehicles (in millions) as a function of t, the number of years since 2000. Use the general exponential form. v(t) = | 202 ( 1.045 )t- (b) Write a formula for the number of people (in millions) as a function of t, the number of years since 2000. Use the general exponential form P(t) (c) If the growth rates remain constant, when is there, on average, one vehicle per person? Give your answer in exact form and decimal form Exact formm years since 2000 Decimal form (nearest tenth): years since 2000

Explanation / Answer

b) P (t) = Po (1 + r)^t

P(t) = 279 ( 1.01)^t

c) 202 (1.045)^t = 279(1.01)^t

exact form is

t = ln ( 279 / 202) / ln ( 1.045 / 1.01) years since 2000

decimal form is

t = 9.5 years since 2000

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