Car Trade-In Problem: Major purchases, like cars, depreciate in value. That is, as time

Chapter 7, Problem 4

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Car Trade-In Problem: Major purchases, like cars, depreciate in value. That is, as time passes, their value decreases. A reasonable mathematical model for the value of an object that depreciates assumes that the instantaneous rate of change of the objects value is directly proportional to the value. a. Write a differential equation that says that the rate of change of a cars trade-in value is directly proportional to that trade-in value. Integrate the equation and express the trade-in value as a function of time.b. Suppose you own a car whose trade-in value is presently $4200. Three months ago itstrade-in value was $4700. Find theparticular equation that expresses thetrade-in value as a function of time since thecar was worth $4200.c. Plot the graph of trade-in value versus time.Sketch the result.d. What will the trade-in value be one year afterb. Suppose you own a car whose trade-in valuethe time the car was worth $4700?e. You plan to get rid of the car when its trade-invalue drops to $1200. When will this be?f. At the time your car was worth $4700, it was31 months old. What was its trade-in valuewhen it was new?g. The purchase price of the car when it wasnew was $16,000. How do you explain thedifference between this number and youranswer to part f ?