Question

dr. hall is studying an endangered fox whose population is declining by 20% every year. if there are currently 3,746 foxes, how many will remain in 4 years? if necessary, round your answer to the nearest whole number.

Explanation:

Step1: Define remaining population rate

Each year, 80% of foxes remain: $1 - 0.20 = 0.80$

Step2: Set up population formula

Use exponential decay: $P(t) = P_0 \times (0.80)^t$
Where $P_0=3746$, $t=4$

Step3: Calculate the population

$$P(4) = 3746 \times (0.80)^4$$
$$(0.80)^4 = 0.4096$$
$$P(4) = 3746 \times 0.4096$$
$$P(4) = 1534.3616$$

Step4: Round to whole number

Round 1534.3616 to nearest integer.

Answer:

1534 foxes