Mathematics

Question

You research the cost of a gallon of gasoline over several years to look for a trend. The table shows your data. The line of best fit uses years since 1980 as the input value. What is a line of best fit for the data? Based upon these prices, how much would you expect to pay in 2028?

Year: 1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012

Price/gallon: $1.25, $1.27, $1.05, $1.28, $1.43, $1.68, $2.11, $3.72, $3.99

A.) y= 0.087x+2.26; $6.44
B.) y= 0.087x+0.587; $4.76
C.) y= 0.134x+1.25; $7.68
D.) y= 0.0347x+0.856; $2.52

1 Answer

  • Answer:

    B.) y= 0.087x+0.587; $4.76

    Step-by-step explanation:

    Without doing a lot of work, you can weed out the answer choices that don't make any sense.

    The approximately $2.75 rise in price in 32 years is about $0.90 per year (to 1 significant digit), so rules out answer choices C and D.

    The low-end prices near $1 rule out answer choice A, which has a y-interecept well above the $1 range. That leaves answer choice B.

    _____

    If you go to the trouble to enter the data into a calculator and have it give you the line of best fit, you find it is about ...

    ... y = 0.867917x +0.586889 . . . . . matches selection B

    and this equation gives you a value for x=48 (year 2028) that is $4.75. Rounding the equation coefficients before you use them will give a different value for the year 2028.

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