The llama population on an island is decreasing by 10 percent per year. Use an exponential equation find the population after 10 years if the population started with 50,000 llamas at the end of year 1.(1 point)

Question

Responses

17,433
17,433

15,690
15,690

19,371
19,371

49,900

Answer 1

To find the llama population after 10 years with an initial population of 50,000 and a decrease of 10% per year, we can use the formula for exponential decay:

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

Where:

• \( P(t) \) = the population at time \( t \)
• \( P_0 \) = the initial population
• \( r \) = the rate of decrease (as a decimal)
• \( t \) = time in years

Given:

• \( P_0 = 50,000 \)
• \( r = 0.10 \)
• \( t = 10 \)

Now we can plug in the values:

\[ P(10) = 50,000 \times (1 - 0.10)^{10} \]

Calculating:

\[ P(10) = 50,000 \times (0.90)^{10} \]

Now compute \( (0.90)^{10} \):

\[ (0.90)^{10} \approx 0.3487 \]

Now calculate \( P(10) \):

\[ P(10) \approx 50,000 \times 0.3487 \approx 17,435 \]

The calculated population after 10 years, rounded to the nearest whole number, is approximately 17,435. Among the provided options, the closest value is:

17,433