Question

In​ 2000, the population of a country was approximately 6.13 million and by 2015 it is projected to grow to 7 million. Use the exponential growth model Upper A equals Upper A 0 e Superscript kt​, in which t is the number of years after 2000 and Upper A 0 is in​ millions, to find an exponential growth function that models the data.

Answer 1

A = 6.13e^(0.00884769t)

Explanation:

The exponential growth model can be written two ways. Comparing them, we can find the value of k.

A = 6.13×(7.00/6.13)^(t/(2015-2000)) = 6.13×e^(kt)

Dividing by 6.13 and taking natural logs, we get ...

t/15×ln(7.00/6.13) = kt

k = ln(7.00/6.13)/15 . . . . . divide by t

k ≈ 0.00884769

Then the exponential growth function can be written as ...

A = 6.13e^(0.00884769t)