To find the population of mountain lions in 2032 given that the current population is 32,873 and it decreases by 10% each year, we can use the formula for exponential decay:
\[ P(t) = P_0 \times (1 - r)^t \]
where:
- \( P(t) \) is the population at time \( t \),
- \( P_0 \) is the initial population,
- \( r \) is the rate of decrease (in decimal form),
- \( t \) is the number of years.
In this case:
- \( P_0 = 32,873 \)
- \( r = 0.10 \) (10% decrease translates to a factor of 0.90 each year),
- \( t = 2032 - 2024 = 8 \) years.
Now we can plug in the values:
\[ P(8) = 32,873 \times (1 - 0.10)^8 \] \[ P(8) = 32,873 \times (0.90)^8 \] \[ P(8) = 32,873 \times 0.43046721 \quad \text{(approximately)} \] \[ P(8) \approx 32,873 \times 0.43046721 \approx 14,137.81 \]
Since the population must be a whole number, we round it to the nearest whole number:
\[ P(8) \approx 14,138 \]
Based on rounding, the closest answer from the provided options is 14150.
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