There are 32,873 mountain lions in the U.S. in 2024. The population of mountain lions is decreasing by 10% every year. How many mountain lion will there be in 2032?

17470

14150

21567

70466

1 answer

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.