Final answer:
To find the future population after 9 years at a 2% decreasing rate, use the exponential decay formula. The expected population after 9 years is approximately 24,052 people.
Step-by-step explanation:
To calculate the future population given a decreasing rate, you can use the formula for exponential decay, which is:
P(t) = P0 e-rt.
Where:
- P(t) is the population at time t,
- P0 is the initial population,
- r is the rate of decrease, and
- t is time in years.
In this case, the initial population (P0) is 28,800, the rate of decrease is 2% per year (or 0.02 when expressed as a decimal), and the time (t) is 9 years.
Plugging the values into the formula, we get:
P(9) = 28,800 e-0.02 × 9.
Using a calculator to compute the exponential part leads to the following:
-0.18 ≈ 28,800 × 0.8353 ≈ 24,052.
Therefore, after 9 years, the population is expected to be approximately 24,052 people.