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](https://tex.z-dn.net/?f=P%3Da%281%2Br%29%5Et)
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}](https://tex.z-dn.net/?f=P%3Da%281%2B0.015%29%5E%7B20%7D)
![P=a(1.015)^{20}](https://tex.z-dn.net/?f=P%3Da%281.015%29%5E%7B20%7D)
![P=1.346855a](https://tex.z-dn.net/?f=P%3D1.346855a)
Where, a is the initial population.
The total percentage increase over the 20 years is
![\% change=\frac{P-a}{a}\times 100](https://tex.z-dn.net/?f=%5C%25%20change%3D%5Cfrac%7BP-a%7D%7Ba%7D%5Ctimes%20100)
where, P is population after 20 years and a is initial amount.
![\% change=\frac{1.346855a-a}{a}\times 100](https://tex.z-dn.net/?f=%5C%25%20change%3D%5Cfrac%7B1.346855a-a%7D%7Ba%7D%5Ctimes%20100)
![\% change=\frac{0.346855a}{a}\times 100](https://tex.z-dn.net/?f=%5C%25%20change%3D%5Cfrac%7B0.346855a%7D%7Ba%7D%5Ctimes%20100)
![\% change=0.346855\times 100](https://tex.z-dn.net/?f=%5C%25%20change%3D0.346855%5Ctimes%20100)
![\% change=34.6855](https://tex.z-dn.net/?f=%5C%25%20change%3D34.6855)
![\% change\approx 34.69](https://tex.z-dn.net/?f=%5C%25%20change%5Capprox%2034.69)
Therefore the population increased by 34.69% over 20 years.