Question

Ethology: The population, P, of fish in a lake t months after a nearby chemical factory commenced operation is given by P = 600(2 + e^-0.2t). Find the number of fish in the lake

(i) in the long run (that is, as t becomes very large).​

Answer 1

The number of fish in the lake is given by the equation P = 600(2 + e^-0.2t).

When t = 0, the number of fish is P = 600(2 + e^0) = 600(2 + 1) = 1200.

Therefore, there are 1200 fish in the lake.

As time goes on, the number of fish will decrease exponentially. This is because the chemical factory is polluting the lake, which is killing the fish.

In 10 months, the number of fish will be P = 600(2 + e^-0.2*10) = 600(2 + 0.125) = 750.

In 20 months, the number of fish will be P = 600(2 + e^-0.2*20) = 600(2 + 0.0625) = 675.

As you can see, the number of fish is decreasing rapidly. In just 20 months, the number of fish will have decreased by more than half.