Question

A population declines by 0.7% each year. By what percentage does it decline each decade? (Round your answer to two decimal

places.)
X %

Answer 1

6.78%

Explanations;

If a population declines by 0.7% each year, then the remaining population will be (1-0.7%) of the previous year.

This can be expressed after one decade (10 years) as;

`\begin{gathered} p=(1-(0.7)/(100))^(10) \\ p=(1-0.007)^(10) \\ p=(0.993)^(10) \\ p=0.9322 \end{gathered}`

The percentage of decline per decade will be expressed as:

`\begin{gathered} \%decline=1-0.9322 \\ \%decline=0.0678=6.78\% \\ \end{gathered}`

This shows that the population declines each decade by 6.78%