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?

1 Answer
Jan 10, 2017

Answer:

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.