Assume a population of fish grows exponentially.

Question

Assume a population of fish grows exponentially. A pond is stocked initially with 500 fish. After 9 months, there are 1,000 fish in the pond. The owner will allow his friends and neighbors to fish on his pond after the fish population reaches 10,000. After how many months will the owner’s friends be allowed to fish?

Answer 1

1000 = 500e^9k

2 = e^9k

ln 2 = 9k

0.6931 ≈ 9k

0.0770 ≈ k

10000 = 1000e^0.0770t

10 = e^0.0770t

ln 10 = 0.0770t

2.3026 ≈ 0.0770t

29.9 ≈ t

In another 30 months they can fish.

Answer 2

38.9 months