The size of a certain insect population is given by $P(t)=100 e^{.02 t}$, where $t$ is measured in days. At what time will the population equal $500 ?$
Answer
Final Answer: The insect population will reach 500 after approximately \(\boxed{80.47}\) days.
Step 1 ：We are given the function \(P(t)=100 e^{.02 t}\) and we need to find the value of \(t\) when \(P(t) = 500\). This is a simple equation solving problem. We can solve it by setting \(P(t)\) equal to \(500\) and solving for \(t\).
Step 2 ：The solution to the equation has returned a value of approximately 80.47 for \(t\). This means that the insect population will reach 500 after approximately 80.47 days.
Step 3 ：Final Answer: The insect population will reach 500 after approximately \(\boxed{80.47}\) days.
