A population is increasing according to the exponential function $y=2 e^{0.04 x}$, where $y$ is in millions and $x$ is the number of years. How long will it take for the population to triple? Which of the following is the correct procedure to answer the question?
A. Evaluate $y=2 e^{0.04(1 / 3)}$
C. Evaluate $y=2 e^{0.04(3)}$.
B. Solve $2 e^{0.04 x}=6$.
D. Solve $2 e^{0.04 x}=3$.
Answer
Final Answer: It will take approximately \(\boxed{27.47}\) years for the population to triple.
Step 1 ：The question asks for the time it will take for the population to triple. This means that the population will grow from 2 million to 6 million. Therefore, we need to solve the equation \(2 e^{0.04 x}=6\) for \(x\). This corresponds to option B.
Step 2 ：Solving the equation gives us the time it will take for the population to triple.
Step 3 ：Final Answer: It will take approximately \(\boxed{27.47}\) years for the population to triple.
