Exponential Growth

Question

The growth model A= 2e^0.002t describes the population, A, of a country in millions, t years after 2003. How long will it take the country to double its population?

Answer 1

A(t) = 2e^0.002t

T = doubling time

A(T) = 2A(0),

where time t=0 is the year 2003.

A(0) = 2

A(T) = 2e^0.002T = 2A(0) = 2(2) = 4

2e^0.002T = 4

e^0.002T = 2

0.002T = ln2

T = (ln2 / 0.002) years = 346.6 years