Question

1 numeric 1 point
a population of 678 frogs increases at an annual rate of 12%. how many frogs will there be after 15 years?
(round your answer to the nearest whole number)

Explanation:

Step1: Recall compound growth formula

The formula for compound population growth is $P = P_0(1 + r)^t$, where $P_0$ is initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Identify given values

$P_0 = 678$, $r = 0.12$, $t = 15$

Step3: Substitute values into formula

$P = 678(1 + 0.12)^{15}$

Step4: Calculate $(1.12)^{15}$

$(1.12)^{15} \approx 5.473565759$

Step5: Compute final population

$P \approx 678 \times 5.473565759$
$P \approx 3711.077585$

Step6: Round to nearest whole number

Round $3711.077585$ to the nearest integer.

Answer:

3711