Questions: A population of deer is increasing at a rate of 12% per year. If this rate of growth remains the same and the population starts out with 250 deer, approximately how many deer will there be after 5 years? a.) 265 deer b.) 508 deer c.) 387 deer d.) 441 deer

Solution Steps

The initial population of deer is given as 250. The growth rate is 12% per year.

The formula for the population after \( n \) years in a geometric sequence is given by: \[ P_n = P_0 (1 + r)^n \] where:

• \( P_n \) is the population after \( n \) years,
• \( P_0 \) is the initial population,
• \( r \) is the growth rate,
• \( n \) is the number of years.

Given:

• \( P_0 = 250 \)
• \( r = 0.12 \)
• \( n = 5 \)

Substitute these values into the formula: \[ P_5 = 250 (1 + 0.12)^5 \]

First, calculate \( 1 + 0.12 \): \[ 1 + 0.12 = 1.12 \]

Next, raise 1.12 to the power of 5: \[ 1.12^5 \approx 1.7623 \]

Finally, multiply by the initial population: \[ P_5 = 250 \times 1.7623 \approx 440.575 \]

Final Answer