Chapter 5.2, Problem 2E

Savings Account Let $A\left(t\right)$ be the balance in a savings account after $t$ years, and suppose that $A\left(t\right)$ satisfies the differential equation

$A\text{'}\left(t\right)=0.045A\left(t\right)$, $A\left(0\right)=3000$

a. How much money was originally deposited in the account?

b. What interest rate is being earned?

c. Find the formula for $A\left(t\right)$.

d. What is the balance after $5$ years?

e. Use part (d) and the differential equation to determine how fast the balance is growing after $5$ years.

f. How large will the balance be when it is growing at the rate of $\$270$ per year?