Automobile production. Using quadratic regression on a graphing calculator, show that the...

Automobile production. Using quadratic regression on a graphing calculator, show that the quadratic function that best fits the data on market share in Problem 1 is

f(x) = −0.0169x2 + 0.47x + 17.1

Problem 1

Automobile production. The table shows the retail market share of passenger cars from Ford Motor Company as a percentage of the U.S. market.

A mathematical model for this data is given by

f(x) = −0.0169x2 + 0.47x + 17.1

where x = 0 corresponds to 1980.

(A) Complete the following table. Round values of f (x) to one decimal place.

x	Market Share	f(x)
0	17.2
5	18.8
10	20.0
15	20.7
20	20.2
25	17.4
30	16.4

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(B) Sketch the graph of f and the market share data in the same coordinate system.

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(C) Use values of the modeling function f to estimate Ford’s market share in 2020 and in 2025.

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(D) Write a brief description of Ford’s market share from 1980 to 2010.