A financial manager is calculating the required annual interest rate for a capital project fund. The fund starts with 10,000 and must grow to 150,000 over 29 years using the continuous compounding formula $A = Pe^{rt}$. Arrange the following steps in the correct order to solve for the interest rate $r$.

A financial advisor is calculating the interest rate $r$ required for a client's retirement fund to reach a specific goal using the continuous compounding formula $A = Pe^{rt}$. After substituting the known values, the advisor simplifies the calculation to the equation ${}15 = e^{29r}$. According to the properties of logarithms, which of the following represents the correct next step to isolate the rate $r$?

A financial advisor is helping a client plan for retirement using the continuous compound interest formula $A = Pe^{rt}$. The client wants to know what interest rate is required for an initial deposit of 10,000 to grow into 150,000 over a period of 29 years. Match each variable from the formula to its specific role in this financial plan.

A business analyst is using the continuous compound interest formula $A = Pe^{rt}$ to determine the annual interest rate required for a corporate investment. To isolate the variable $r$ from the exponent when the other values are known, the analyst must apply the ____ logarithm to both sides of the equation.

To determine the required interest rate $r$ for a corporate investment using the continuous compounding formula $A = Pe^{rt}$, a financial planner must apply the common logarithm ($\log$) to both sides of the equation after dividing the final amount by the principal.