Question 1
You deposit $\$ 3000$ in an account earning $8 \%$ interest compounded continuously. How much will you have in the account in 10 years?
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Step 1 ：Given that the principal amount (P) is $3000, the annual interest rate (r) is 8% or 0.08 in decimal, and the time (t) is 10 years.

Step 2 ：The formula for continuous compound interest is \(A = Pe^{rt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substitute the given values into the formula: \(A = 3000 * e^{0.08*10}\)

Step 4 ：Simplify the exponent in the equation: \(A = 3000 * e^{0.8}\)

Step 5 ：Calculate the value of \(e^{0.8}\), which is approximately 2.22554.

Step 6 ：Substitute this value back into the equation: \(A = 3000 * 2.22554\)

Step 7 ：\(\boxed{A = 6676.62}\), so after 10 years, you will have approximately $6676.62 in the account.