Answer
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Work Step by Step
$P(t)=500e^{0.02t},$
a. $P(0)=500e^{0.02t}=500$
b. From the formula $P(t)=500e^{0.02t},$ the growth rate of the population of insect is $0.02$ in $t$ years with initial population of $500$.
c. $P(10)=500e^{0.2}=610.7$
d. $P(t)=500e^{0.02t}=800,$
$e^{0.02t}=1.6,$
$0.02t=\ln{1.6},$
$t=23.5$
e.
$P(t)=500e^{0.02t}=1000,$
$e^{0.02t}=2,$
$0.02t=\ln 2,$
$t=34.66$
