Question

The population of geckos in a reptile habitat can be represented by the expression s(1.35)t, where s is the initial number of geckos and t is the time, in years. What is the approximate equivalent quarterly growth rate of the geckos?
A)7.79%
B)8.75%
C)2.53%
D)33.75%

Answer 1

The formular for an exponential population growth is given by

$P(t) = P_0(1 + r)^t$

where: r is the rate per period, t is the time and $P_0$ is the initial population.

Comparing the above formular with the given formula we have

$s(1.35)^t=s(1+0.35)^t \\ \\ r=0.35\ or\ 35%$

Therefore, the equivalent quarterly growth rate of the geckos is 8.75%.