Question

The population of a nearly extinct species is decreasing exponentially.

Answer 1

Exponential growth/decay is modeled by the differential equation,
\[\frac{dy}{dt}=ky\]
and hence its general solution,
\[y(t)=Ce^{kt}\]
which describes growth if \(k>0\) and decay if \(k<0\).

Notice that when \(t=0\) (at the initial time), you have \(y(0)=Ce^0=C\), which would indicate that \(C\) is the initial population.

So, when \(C=350\), and you know that after five years (\(t=5\)) the population drops to \(y(5)=320\), you have the following equation:
\[320=350e^{5k}\]
From here, you can solve for \(k\), then plug into the DE and figure out the rate of decrease.

Answer 2

What is DE?

Answer 3

"Differential equation"