The table shows the time t (in seconds) required for a car to attain a speed of s miles per hour from a standing start.
Speed, s Time, t
30.......................................3.4
40.......................................5.0
50.......................................7.0
60.......................................9.3
70.....................................12.0
80.....................................15.8
90.....................................20.0
Two models for these data are given below.
t1 = 40.757 + 0.556s − 15.817 ln s
t2 = 1.2259 + 0.0023s2
(a) Use the regression feature of a graphing utility to find a linear model t3 and an exponential model t4 for the data.
(b) Use the graphing utility to graph the data and each model in the same viewing window.
(c) Create a table comparing the data with estimates obtained from each model.
(d) Use the results of part (c) to find the sum of the absolute values of the differences between the data and the estimated values found using each model. Based on the four sums, which model do you think best fits the data? Explain.