Question

Bikini Bottom had a population of 15,000 fish. Due to the noise of Squidward's awful Clarinet practicing, the fish have been leaving the city at a rate of 7% annually. Approximately how long will it take for the population to drop to 10,000 fish.

Answer 1

It will take approximately 10.24 years for the population of fish to reduce from 15,000 to 10,000 due to a 7% annual decline caused by Squidward's clarinet practicing.

Step-by-step explanation:

The question asks about the time it will take for a population of 15,000 fish in Bikini Bottom to reduce to 10,000 if they are leaving at a rate of 7% annually due to the noise of Squidward's clarinet practicing. This problem can be solved using the concept of exponential decay. The formula used for calculating the time (t) in such scenarios is:

t = (ln(remaining population / initial population)) / (ln(1 - rate of decline))

In this scenario, the initial population (P0) is 15,000, the remaining population (P) we want to reach is 10,000, and the annual rate of decline is 7% or 0.07. Plugging into the formula:

t = (ln(10,000 / 15,000)) / (ln(1 - 0.07))

After calculating:

t ≈ 10.24 years

Therefore, it will take approximately 10.24 years for the fish population to reduce from 15,000 to 10,000.