Depreciation of a New Car Depreciation of a New Car In buying

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2.   Depreciation of a New Car In buying a new car,
     one consideration might be how well the price of the car
     holds up over time. Different makes of cars have different
                                                                                                      Cumulative Review      427

depreciation rates. We will discuss one way of computing        3.   CBL Experiment The following data were collect-
the depreciation rate for a car. Look up the value of your           ed by placing a temperature probe in a cup of hot water,
favorite car for the past 5 years in the NADA (“blue                 removing the probe, and then recording temperature over
book”) available at your local bank or public library or             time. According to Newton’s Law of Cooling, these data
via the Internet. Let t = 0 represent the cost of this car if        should follow an exponential model.
you purchased it new, t = 1 represent the cost of the same           (a) Using a graphing utility, draw a scatter diagram for
car when it is 1 year old, and so on. Fill in the following              the data.
table:                                                               (b) Using a graphing utility, fit an exponential function to
                                                                         the data.
                                                                     (c) Graph the exponential function found in part (b) on
       Year                 Value                                        the scatter diagram.
                                                                     (d) Predict how long it will take for the water to reach a
       t = 0                                                             temperature of 110°F.
       t = 1                                                         (e) Write the model found in part (b) in the form of
                                                                         equation (4) on page 402 if the surrounding temper-
       t = 2
                                                                         ature is 70°F.
       t = 3
                                                                     Time        Temperature (°F)   Time        Temperature (°F)
       t = 4
                                                                      0         175.69              13         148.50
       t = 5
                                                                      1         173.52              14         146.84
                                                                      2         171.21              15         145.33
                                                                      3         169.07              16         143.83

(a) Using a graphing utility, draw a scatter diagram with             4         166.59              17         142.38
    time as the independent variable and value as the                 5         164.21              18         141.22
    dependent variable.
                                                                      6         161.89              19         140.09
(b) Find the exponential function of best fit.
(c) Express this function in the form A = A 0 ert.                    7         159.66              20         138.69
(d) What is the value of A 0 ? Compare this value to the              8         157.86              21         137.59
    purchase price of the vehicle.
                                                                      9         155.75              22         136.78
(e) What is the value of r, the depreciation rate?
(f) Compare your value of r to others in your class.Which            10         153.70              23         135.70
    car has the lowest rate of depreciation? The highest?            11         151.93              24         134.91
(g) How might the depreciation factor into your decision
                                                                     12         150.08              25         133.86
    regarding a new car purchase?

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