Chapter 6.5, Problem 1E

Reminder Round all answers to two decimal places unless otherwise indicated.

Small Business Loan After $t$ years, a small business owes $B$ dollars on a loan. The balance draws a continuous compounding rate of $6\%$ per year, and payments of $\$5000$ per year are made to the lending institution. Then the equation of change for the account balance is given by

$\frac{dB}{dt}=0.06B-5000$

a. Find the equilibrium solution.

b. Explain what is happening at the equilibrium solution in practical terms.

c. If the small business expects to pay off the loan eventually, should $B$ be larger or smaller than the equilibrium solution?