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.

Question

asked Nov 19, 2020 114k views

1 Answer

David Scarlett · Answer 1 · 2020-11-24T16:55:53+0000

Answer:

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.