a population of hippos increases continuously at a rate of 2.10%. if there are 167 hippos at the start of a…

a population of hippos increases continuously at a rate of 2.10%. if there are 167 hippos at the start of a wildlife study, how many should be left after 18 months? round your answer to the nearest whole number.

a population of hippos increases continuously at a rate of 2.10%. if there are 167 hippos at the start of a wildlife study, how many should be left after 18 months? round your answer to the nearest whole number.

Answer

Explanation:

Step1: Convert time to years

18 months = $\frac{18}{12}=1.5$ years.

Step2: Use continuous - growth formula

The continuous - growth formula is $A = Pe^{rt}$, where $P$ is the initial amount, $r$ is the growth rate (in decimal form), and $t$ is the time in years. Here, $P = 167$, $r=0.021$, and $t = 1.5$. $A=167\times e^{0.021\times1.5}$.

Step3: Calculate the exponent

$0.021\times1.5 = 0.0315$.

Step4: Calculate the value of $e^{0.0315}$

Using a calculator, $e^{0.0315}\approx1.03199$.

Step5: Calculate the final amount

$A = 167\times1.03199\approx172$.

Answer:

172