Question

(unit 4) (aks 2d) in the year 2000, inman park in atlanta, ga had a squirrel population of 500. for the next 15 years, the squirrel population grew at a rate of 4.5% per year. what was the squirrel population in the year 2020? a 967 squirrels × b 1205 squirrels c 1206 squirrels d 2250 squirrels

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the annual growth rate (as a decimal), and $t$ is the time in years.

Step2: Determine the values of \( P_0 \), \( r \), and \( t \)

• \( P_0 = 500 \) (initial population in 2000)
• \( r = 4.5\% = 0.045 \) (annual growth rate)
• \( t = 2020 - 2000 = 20 \) years (time from 2000 to 2020)

Step3: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step4: Calculate \( (1.045)^{20} \)

Using a calculator, \( (1.045)^{20} \approx 2.4117 \)

Step5: Calculate the population \( P(20) \)

$$
LATEXBLOCK1
$$

Answer:

C. 1206 squirrels