Question

Based on the model, the solution to the equation `50=40e^( 0.027t)` gives the number of years it will take for the population of country A to reach 50 million. What is the solution to the equation expressed as a logarithm?

Answer 1

Equation expressed as a logarithm is `0.027t=ln50-ln40`

Explanation:

`50=40e^(0.027t)` in regard to the question indicates that the population of the country increases from `40` million to `50` million at a continuous rate of `0.027` or `2.7%` per annum in `t` years.

As `50=40e^(0.027t)`, we have

`e^(0.027t)=50/40`

hence `0.027t=ln50-ln40`, when `ln` means Napiers logrithm i.e. to the base `e`.

This solves as follows:

`t=(ln50-ln40)/0.027=(3.9120-3.6889)/0.027=8.265` years.