Question

a biologist monitors the fish population in an aquarium. there are 400 fish when she begins her study. the number of fish after t days can be modeled by the equation $p = 400e^{0.014t}$. how many days will it take for the fish population to double? round your answer to the nearest whole number. t =

Explanation:

Step1: Set up the equation

The initial population is 400. We want to find when the population doubles, so $P = 800$. Substitute into $P = 400e^{0.014t}$, getting $800=400e^{0.014t}$.

Step2: Simplify the equation

Divide both sides of $800 = 400e^{0.014t}$ by 400. We have $\frac{800}{400}=e^{0.014t}$, which simplifies to $2 = e^{0.014t}$.

Step3: Take the natural - logarithm of both sides

Since $\ln(e^{x})=x$, taking the natural - logarithm of both sides of $2 = e^{0.014t}$ gives $\ln(2)=\ln(e^{0.014t})$, so $\ln(2)=0.014t$.

Step4: Solve for t

We know that $\ln(2)\approx0.6931$. Then $t=\frac{\ln(2)}{0.014}\approx\frac{0.6931}{0.014}\approx49.51$.

Answer:

50