Edward C. answered • 03/19/15

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p(x) is linear so it has the form p(x) = m*x + b and goes thru the points (1970,690) and (5330,780). Find the slope

m = (y

_{2}- y_{1})/(x_{2}- x_{1}) = (780 - 690)/(5330 - 1970) = 90/3360 = 3/112Use the first point (1970,690) and the slope 3/112 to find b

690 = (3/112)*1970 + b

690 = 2955/56 + b

b = 690 - 2955/56 ~ 690 - 52.768 = 637.232

So p(x) = (3/112)*x + 637.23

When p = $710 then

710 = (3/112)*x + 637.23

(3/112)*x = 72.77

x = 72.77*(112/3) = 2716.75 ~ 2717 rounded up

The lowest price is found when x = 1

p(1) = (3/112)*1 + 637.23 = 637.26 = $638 rounded up