Question

Solve for k .

A country’s population in 1993 was 107 million . In 1999 it was 112 million . Estimate the population in 2017 using the exponential growth formula. Round your answer to the nearest million. P=Ae^kt.

Answer 1

Using the given numbers, you can write the exponential function as
P = 107*(112/107)^(t/6)
where t = years since 1993.

This can be written in the form
P = 107*e^(kt)
where
k = ln(112/107)/6
k ≈ 0.00761167 . . . . . . . your value of k


The population in 2017 by this model is
107*e^(0.00761167*(2017 -1993)) ≈ 128.446

The growth formula estimates the 2017 population at 128 million.