Question

A countrys population in 1990 was 145 million. In 1998 it was 151 million. Estimate the population in 2015 using the exponential growth formula. Round your answer to the nearest million

Answer 1

The population in 2015 will be 165 million.

Explanation:

The exponential growth formula is given by:

`f(t) = a(1 + r)^(\Delta t)`

Where:

a: is the initial population

r: is the rate of increase

Δt: is the time

With the initial information we can find the rate:

`151 = 145(1 + r)^(1998-1990)`

Using logarithm:

`ln(151) = ln(145) + 8[ln(1 + r)]`

`ln(1 + r) = (ln(151) - ln(145))/(8)`

`ln(1 + r) = 5.0683 \cdot 10^(-3)`

Using exponential:

`e^(ln(1 + r)) = e^{5.0683 \cdot 10^(-3)}`

`r = 5.081 \cdot 10^(-3)`

Now, we can find the estimated population in 2015:

`f(t) = 151(1 + 5.081 \cdot 10^(-3))^(2015-1998)`

`f(t) = 165`

Therefore, the population in 2015 will be 165 million.

I hope it helps you!