Discuss the solution in the context of the initial topic. Write the solution of the differential equation in terms of the initial Question. Describe how this could be useful for someone in the field from which the model was obtained. Include solution values or graphics to illustrate the utility and applicability of the solution in the context of the Question below.

Discuss what you learned from the modeling process. Write one to two paragraphs pertaining to what you can take away from the modeling process in general.

Example 3: Paying off a loan A similar situation is paying off a loan. Suppose that you took out college loans totaling $60, 000 with interest of 7.5%. You have an online payment plan which continuously deducts money from your bank account at a rate which comes out to $15, 000 per year. How long will it take you to pay off the loan? Again, this will be a rst-order linear differential equation. The change in the balance of the loan will go up as interest is accumulated, and go down as payments are made. As such, if 3:; represents the balance of the loan at time t, then the differential equation will have a positive term for the interest, and a negative term for the payments: y' = .0753: 15000 Again, the initial condition tells us that 11(0) = 60000. Using the techniques from class, we get the general solutlon POE) = 200000 + 0907\" and particular solution P0?) = 200000 1400006075\" In order to nd the amount of time it takes to pay off the loan, we need to solve for when the balance P(t) is zero. 0 = 200000 1400009073 200000 = 1400006075\" 200000 _ 9 _ 9075* 140000 _ 7 _