Question 7

You deposit $\mathrm{\$}3100$ in an account earning $7\mathrm{\%}$ 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 $\mathrm{\$}10800$ 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 $\underset{―}{2}2$ decimal places.

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Step 1 ：To solve this problem, we can use the formula for continuous compound interest: $A(t)=P\ast e^{(}rt)$

Step 2 ：For the first question, we have: $P=\$3100$, $r=7$, $t=15$ years

Step 3 ：Plugging these values into the formula, we get: $A(15)=3100\ast e^{(}0.07\ast 15)$

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: $P=\$3100$, $r=7$, $A(t)=\$10,800$

Step 6 ：We need to solve for $t$ in the equation $A(t)=3100\ast e^{(}0.07\ast t)=10800$

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.