Question

The population of a certain type of gorilla has been decreasing at a rate of about 3.5% per year over the past twenty years. If there are currently about 250 of theses gorillas, how many were there 20 years ago? (round your answer to the whole number)Immersive Reader

Answer 1

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:

$n(t) = n_0 (1+r)^t$

where

n(t) is the number of gorillas after t years

$n_0$ 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:

$n(t)=250$ is the number of gorillas when t = 20 years

$r=-\frac{3.5}{100}=-0.035$ is the grow rate of the population

So the equation becomes:

$250 = n_0 (1-0.035)^{20} = n_0 (0.965)^{20}$

And solving for $n_0$, we find the initial number of gorillas:

$250=n_0 (0.965)^{20}=n_0 \cdot 0.490\\n_0 = \frac{250}{0.490}=510$