Question

the population of deer in yosemite valley has an annual growth rate of 8% per year. if there were a total of 22,400 deer in the year 2019, how many will there be predicted in the year 2029? round your answer to the nearest whole number.

Explanation:

Step1: Identify the growth - formula

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

Step2: Convert the growth rate to a decimal and find $t$

The growth rate $r=8\%=0.08$. The number of years from 2019 to 2029 is $t = 2029 - 2019=10$ years, and the initial population $P_0 = 22400$.

Step3: Substitute values into the formula

Substitute $P_0 = 22400$, $r = 0.08$, and $t = 10$ into the formula $P = P_0(1 + r)^t$. So $P=22400\times(1 + 0.08)^{10}$.

Step4: Calculate $(1 + 0.08)^{10}$

$(1 + 0.08)^{10}=1.08^{10}\approx2.158925$.

Step5: Calculate the final population

$P=22400\times2.158925\approx48359$.

Answer:

48359