Chapter 10.1, Problem 16E

Savings Account Let $f\left(t\right)$ be the balance in a savings account at the end of $t$ years, and suppose that $y=f\left(t\right)$ satisfies the differential equation $y\text{'}=0.04y-2,000$.

a. If after $1$ year, the balance is $\$10,000$, is it increasing or decreasing at that time? At what rate is it increasing or decreasing at that time?

b. Write the differential equation in the form $y\text{'}=k\left(y-M\right)$.

c. Describe the differential equation in words.