In 2000, there were about 208 million vehicles and about 281 million people in a
ID: 2912347 • Letter: I
Question
In 2000, there were about 208 million vehicles and about 281 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 1% 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) =
(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 form: years since 2000
Decimal form (nearest tenth): years since 2000
Explanation / Answer
a) formula for number of vehicles
V(t) = 208 e^.045 t
b) formula for number of people
P(t) = 281 e^.01 t
c) setting the two equations equal
208 e^.045 t = 281 e^.01 t
208/281 e^.045t = e^.01t
.7402 e^.045t = e^.01t
t = 8.6
so after 8.6 years there will be one vehicle / person
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