Use the formula t=ln2/k that gives the time for a population, with a growth rate k, to double, to answer the following question.

The growth modes A=8e^0.005t describes the population, A, of a country in millions, t years after 2003.

What is the countries growth rate? How long will it take the country to double its population?

k = 0.005 doubling time ≈ 139 years

Step-by-step explanation:

Matching the form

A = A0·e^ (kt)

to the given equation

A = 8·e^ (.005t)

we can identify the value of k as being 0.005.

k = 0.005

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The doubling time is given by the formula ...

t = ln (2) / k = ln (2) / 0.005 ≈ 138.63

It will take about 139 years for the population to double.