Question 7 You deposit $\$ 3100$ in an account earning $7 \%$ interest compounded continuously. Give the function that describes this situation. Use A(t) as your output. How much will you have in the account in 15 years? \$ Round your answer to 2 decimal places. How long will it be until you have $\$ 10800$ in the account? years. Round your answer to 2 decimal places. How long does it take for the money in the account to double? years. Round your answer $\underline{2} 2$ decimal places. Question Help: Message instructor Check Answer
Solution
Step 1 ：To solve this problem, we can use the formula for continuous compound interest: \(A(t) = P * e^(rt)\)
Step 2 ：For the first question, we have: \(P = $3100\), \(r = 7% = 0.07\), \(t = 15\) years
Step 3 ：Plugging these values into the formula, we get: \(A(15) = 3100 * e^(0.07 * 15)\)
Step 4 ：Calculating this, we find that after 15 years, you will have approximately $8,019.47 in the account.
Step 5 ：For the second question, we have: \(P = $3100\), \(r = 7% = 0.07\), \(A(t) = $10,800\)
Step 6 ：We need to solve for \(t\) in the equation \(A(t) = 3100 * e^(0.07 * t) = 10800\)
Step 7 ：Solving this equation, we find that it will take approximately 20.47 years until you have $10,800 in the account.
Step 8 ：For the third question, we need to find the time it takes for the money in the account to double.
Step 9 ：Setting up the equation \(A(t) = 2P\) and solving for \(t\), we get: \(t = ln(2) / 0.07\)
Step 10 ：Calculating this, we find that it takes approximately 9.90 years for the money in the account to double.
