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 amount of the population after time $t$,
• $P$ is the initial population,
• $r$ is the annual growth rate (in decimal form),
• $t$ is the time in years.

Here, $P = 6004$, $r = 0.08$ (since 8% = 0.08), and $t = 10$.

Step2: Substitute the values into the formula

Substitute $P = 6004$, $r = 0.08$, and $t = 10$ into the formula:
$A = 6004(1 + 0.08)^{10}$

Step3: Calculate $(1 + 0.08)^{10}$

First, calculate $1.08^{10}$. Using a calculator, $1.08^{10} \approx 2.158925$.

Step4: Multiply by the initial population

Multiply 6004 by 2.158925:
$A = 6004 \times 2.158925 \approx 6004 \times 2.158925$

Calculate $6004 \times 2.158925$:
$6004 \times 2.158925 \approx 12962.1857$

Step5: Round to the nearest whole number

Rounding 12962.1857 to the nearest whole number gives 12962.

Answer:

12962