Question

alex is studying the population of deer in a national park. he found that over the last 10 years, the population had increased by 18%, with a margin of error of ±2.5%. if the initial population of deer was 1,200, estimate the total population range after 10 years, considering the margin of error.

Explanation:

Step1: Calculate the lower - bound percentage

The lower - bound of the percentage increase is $18\% - 2.5\%=15.5\% = 0.155$.

Step2: Calculate the lower - bound population

The formula for population increase is $P = P_0(1 + r)$, where $P_0$ is the initial population and $r$ is the rate of increase. So the lower - bound population $P_{lower}=1200\times(1 + 0.155)=1200\times1.155 = 1386$.

Step3: Calculate the upper - bound percentage

The upper - bound of the percentage increase is $18\%+2.5\% = 20.5\%=0.205$.

Step4: Calculate the upper - bound population

Using the population increase formula, the upper - bound population $P_{upper}=1200\times(1 + 0.205)=1200\times1.205 = 1446$.

Answer:

The population range is from 1386 to 1446 deer.