Question

An animal reserve has 20,000 elk. The

population is increasing at a rate of 8% per
year. There is a concern that the food will be
scarce when the population doubles. How
long will it take for the population to reach
40,000. Show and explain your work.

Answer 1

`\\ \rm\Rrightarrow P(1+r)^n=I`

• P is principal
• R is rate if interest
• I is final amount

`\\ \rm\Rrightarrow 20000(1+0.08)^n=40000`

`\\ \rm\Rrightarrow (1.08)^n=2`

`\\ \rm\Rrightarrow log(1.08)^n=log2`

`\\ \rm\Rrightarrow nlog1.08=log2`

`\\ \rm\Rrightarrow n(0.033)=0.3`

`\\ \rm\Rrightarrow n=3(3)=9`

Answer 2

9 years

Explanation:

by using the formula :

20,000(1 + 0.08) ^n = 40,000

=> (1.08)^n = 40,000/20, 000

(1.08) ^n = 2

n = 9