Respuesta :
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:
[tex]P=a(1+r)^t[/tex]
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
[tex]P=a(1+0.015)^{20}[/tex]
[tex]P=a(1.015)^{20}[/tex]
[tex]P=1.346855a[/tex]
Where, a is the initial population.
The total percentage increase over the 20 years is
[tex]\% change=\frac{P-a}{a}\times 100[/tex]
where, P is population after 20 years and a is initial amount.
[tex]\% change=\frac{1.346855a-a}{a}\times 100[/tex]
[tex]\% change=\frac{0.346855a}{a}\times 100[/tex]
[tex]\% change=0.346855\times 100[/tex]
[tex]\% change=34.6855[/tex]
[tex]\% change\approx 34.69[/tex]
Therefore the population increased by 34.69% over 20 years.
