Question

the rabbit population in butler county, which is currently at 6,004 rabbits, is increasing by 8% each year. how many rabbits will there be in 10 years? if necessary, round your answer to the nearest whole number. rabbits

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is \( A = P(1 + r)^t \), where \( A \) is the final amount, \( P \) is the initial principal amount, \( r \) is the annual growth rate (in decimal), and \( t \) is the time in years.

Step2: Convert the growth rate to decimal

The growth rate \( r = 8\% = 0.08 \).

Step3: Identify the values of \( P \), \( r \), and \( t \)

Here, \( P = 6004 \), \( r = 0.08 \), and \( t = 10 \).

Step4: Substitute the values into the formula

\( A = 6004(1 + 0.08)^{10} \)
First, calculate \( (1 + 0.08)^{10} \). \( 1.08^{10}\approx2.158925 \)
Then, multiply by \( 6004 \): \( A = 6004\times2.158925 \approx 12963.1857 \)

Step5: Round to the nearest whole number

Rounding \( 12963.1857 \) to the nearest whole number gives \( 12963 \).

Answer:

12963