Question

A population of 450 animals decreases at an annual rate of 16% a year. How long before there are only 100 animals left, and what is the method to determine this time?

Answer 1

To determine how long it takes for the population to reach 100 animals, use the formula for exponential decay: Final Population = Initial Population * (1 - Rate)^Time. Solve for Time to find that it takes approximately 9.4 years.

Step-by-step explanation:

To determine how long it takes for the population to reach 100 animals, we can use the formula for exponential decay. The formula is given by:

Final Population = Initial Population * (1 - Rate)^Time

Where the Final Population is 100, the Initial Population is 450, and the Rate is 16% (or 0.16), and we need to solve for Time. Rearranging the formula to solve for Time, we get:

Time = log((Final Population / Initial Population), (1 - Rate))

Substituting the given values, we get:

Time = log((100 / 450), (1 - 0.16))

Using a calculator, we can find that the time it takes for the population to reach 100 animals is approximately 9.4 years.