Chapter 5.2, Problem 1E

Savings Account Let $A\left(t\right)=5000e^{0.04t}$ be the balance in a savings account after $t$ years.

a. How much money was originally deposited?

b. What is the interest rate?

c. How much money will be in the account after $10$ years?

d. What differential equation is satisfied by $y=A\left(t\right)$?

e. Use the results of parts (c) and (d) to determine how fast the balance is growing after $10$ years.

f. How large will the balance be when it is growing at the rate of $\$280$ per year?