Question

If a population of dolphins increases at a constant rate of 1.5% every year for 20 years what will be the total percentage increase over the 20 years.

Answer 1

The population increased by 34.69% over 20 years.

Explanation:

It is given that the population of dolphins increases at a constant rate of 1.5% every year for 20 years.

Formula for population increase:

`P=a(1+r)^t`

where, a is initial population, r is growth rate and t is time in years.

If the population of dolphins increases at a constant rate of 1.5% every year for 20 years, then the population after 20 years is

`P=a(1+0.015)^(20)`

`P=a(1.015)^(20)`

`P=1.346855a`

Where, a is the initial population.

The total percentage increase over the 20 years is

`\% change=(P-a)/(a)* 100`

where, P is population after 20 years and a is initial amount.

`\% change=(1.346855a-a)/(a)* 100`

`\% change=(0.346855a)/(a)* 100`

`\% change=0.346855* 100`

`\% change=34.6855`

`\% change\approx 34.69`

Therefore the population increased by 34.69% over 20 years.