Consider a loan repayment plan described by the following initial value problem, where the amount borrowed is B(0) = $40,000, the monthly payments are $600, and B(t) is the unpaid balance of the loan. Use the initial value problem to answer

parts a through c.

B' (+) =0.03B - 600, B(0) = 40,000

a) Find the solution of the initial value problem and explain why B is an increasing solution.

B(t) =

Why is B an increasing function?

O A. The function is increasing because it is an exponential function with a positive coefficient and a negative exponent.

O B. The function is increasing because it is an exponential function with a positive coefficient and a positive exponent.

O C. The function is increasing because it is an exponential function with a positive exponent.

O D. The function is increasing because it is an exponential function with a positive coefficient.

b) What is the most that you can borrow under the terms of this loan without going further into debt each month?

The most you could borrow is $

c) Now consider the more general loan repayment plan described by the value problem

B' (t) =rB -m, B(0) = Bo

where r> 0 reflects the interest rate, m > 0 is the monthly payment, and Bo > 0 is the amount borrowed. In terms of m and r, what is the maximum amount Bo that can be borrowed without going further into debt?