The size of a certain insect population is given by $P(t)=100 e^{.03 t}$, where $t$ is measured in days. At what time will the population equal 300 ?
It will take days for the population to equal 300 .
Answer
Final Answer: The time at which the population will equal 300 is approximately \(\boxed{36.63}\) days.
Step 1 ：The size of a certain insect population is given by \(P(t)=100 e^{.03 t}\), where \(t\) is measured in days. We need to find out at what time will the population equal 300.
Step 2 ：We need to solve the equation \(100 e^{.03 t} = 300\) for \(t\). This is an exponential equation, and we can solve it by taking the natural logarithm on both sides of the equation.
Step 3 ：By solving the equation, we find that \(t\) is approximately 36.63.
Step 4 ：Final Answer: The time at which the population will equal 300 is approximately \(\boxed{36.63}\) days.
