---### Doubling Time Calculation for Continuous Compounding#### Problem Statement:1. **Find the time it takes for $5,000 to double when invested at an annual interest rate of 6%, compounded continuously.** - __________ years2. **Find the time it takes for $500,000 to double when invested at an annual interest rate of 6%, compounded continuously.** - __________ years#### Instructions:- **Give your answers accurate to 4 decimal places.**To solve these problems, we can use the formula for continuous compounding:\[ A = P e^{rt} \]Where:- $ A $ is the amount of money accumulated after n years, including interest.- $ P $ is the principal amount (the initial amount of money).- $ r $ is the annual interest rate (decimal).- $ t $ is the time the money is invested for, in years.- $ e $ is the base of the natural logarithm (approximately equal to 2.71828).For the amount to double, $ A = 2P $. The equation becomes:\[ 2P = P e^{rt} \]Dividing both sides by $ P $:\[ 2 = e^{rt} \]Taking the natural logarithm of both sides:\[ \ln(2) = rt \]Solving for $ t $:\[ t = \frac{\ln(2)}{r} \]Given the annual interest rate $ r $ is 6% or 0.06, we can substitute into the formula to find the time $ t $ for each problem.For further assistance, please watch the instructional video by clicking the video link.**Submit your answer by clicking the “Submit Question” button below.**---[Submit Question]---

Find the time it takes for $5,000 to double when invested at an annual interest rate of 6%, compounded continuously. years Find the time it takes for $500,000 to double when invested at an annual interest rate of 6%, compounded continuously. years Give your answers accurate to 4 decimal places. Question Help: Video