Questions: The population is decreasing at a rate of 4% per year. If the population is 28,000 today, what will the population be in 12 years? Round your answer to the nearest whole number, if necessary.

Solution Steps

To solve this problem, we need to calculate the future population given a current population and a constant rate of decrease. This is a classic example of exponential decay. The formula to use is:

\[ P(t) = P_0 \times (1 - r)^t \]

where:

• \( P(t) \) is the future population,
• \( P_0 \) is the current population,
• \( r \) is the rate of decrease (expressed as a decimal),
• \( t \) is the time in years.

1. Identify the current population (\( P_0 = 28000 \)).
2. Convert the percentage rate of decrease to a decimal (\( r = 0.04 \)).
3. Use the exponential decay formula to calculate the population after 12 years.

We are given the current population \( P_0 = 28000 \), the rate of decrease \( r = 0.04 \), and the time period \( t = 12 \) years.

The future population \( P(t) \) can be calculated using the formula:

\[ P(t) = P_0 \times (1 - r)^t \]

Substituting the known values:

\[ P(12) = 28000 \times (1 - 0.04)^{12} \]

Calculating the expression:

\[ P(12) = 28000 \times (0.96)^{12} \approx 28000 \times 0.171556 \]

This results in:

\[ P(12) \approx 17155.873205233478 \]

Rounding \( 17155.873205233478 \) to the nearest whole number gives:

\[ \text{Future Population} \approx 17156 \]

Final Answer