In 2000, there were about 208 million vehicles and about 281 million people in a

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

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.