Answer:
510 gorillas
Step-by-step explanation:
In this problem, the population of gorillas is decreasing at a rate of 3.5 % per year.
We can write an expression for the population of gorillas as follows:
[tex]n(t) = n_0 (1+r)^t[/tex]
where
n(t) is the number of gorillas after t years
[tex]n_0[/tex] is the number of gorillas at t = 0
r is the grow rate of the population
t is the number of years
Here we have:
[tex]n(t)=250[/tex] is the number of gorillas when t = 20 years
[tex]r=-\frac{3.5}{100}=-0.035[/tex] is the grow rate of the population
So the equation becomes:
[tex]250 = n_0 (1-0.035)^{20} = n_0 (0.965)^{20}[/tex]
And solving for [tex]n_0[/tex], we find the initial number of gorillas:
[tex]250=n_0 (0.965)^{20}=n_0 \cdot 0.490\\n_0 = \frac{250}{0.490}=510[/tex]
