decision? 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?