Question

A country's population in 1990 was 46 million.

In 2002 it was 49 million. Estimate
the population in 2006 using the exponential
growth formula. Round your answer to the
nearest million.
P= Aekt

Answer 1

50 million

Explanation:

You don't need to go to the trouble to find the value of k in e^(kt). Rather, you can use the given ratio directly.

When t = years after 1990, the population of 49 million took 12 years to achieve. The estimate desired is for 16 years after the year 1990. The appropriate exponential formula for the population is ...

P = 46·(49/46)^(t/12)

Then for t=16, this is ...

P = 46·(49/46)^(16/12) ≈ 50.04 . . . . million

The population in 2006 is estimated at 50 million.

_____

The form of the exponential equation we used above is ...

f(x) = (baseline value)·(ratio to baseline)^(x/(interval corresponding to ratio))