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

Answer:

The population increased by 34.69% over 20 years.

Step-by-step 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

$\% change=\frac{P-a}{a}\times 100$

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

$\% change=\frac{1.346855a-a}{a}\times 100$

$\% change=\frac{0.346855a}{a}\times 100$

$\% change=0.346855\times 100$

$\% change=34.6855$

$\% change\approx 34.69$

Therefore the population increased by 34.69% over 20 years.