Question

A species of dolphins is decreasing at a rate of 3.1% per year. If there are currently 20,000 dolphins, how many will there be in 30 years?

Answer 1

About 7,776 dolphins

Explanation:

we know that

The equation of a exponential decay function is given by

`y=a(1-r)^x`

where

y is the number of species of dolphins

x is the number of years

a is the initial value

r is the rate of change

we have

`a=20,000\\r=3.1\%=3.1/100=0.031`

substitute

`y=20,000(1-0.031)^x`

`y=20,000(0.969)^x`

How many dolphins will there be in 30 years?

For x=30 years

substitute in the equation

`y=20,000(0.969)^(30)=7,776`