Question 1019231
we use linear regression for this problem
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we want to determine the following formula
c(t) = a + bt
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we have N = 6 pairs of data, first we calculate
tc and t^2 for each pair
t c tc t^2
1 50 50 1
1.5 60 90 2.25 
2 70 140 4
2.5 80 200 6.25
3 90 270 9
3.5 130 455 12.25
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summation of t's   =  13.5
summation of c's   =   480
summation of tc's  =  1205
summation of t^2's = 34.75
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slope(b) = ((N * summation of tc's) - (summation of t's * summation of c's)) / ((N * summation of t^2's) - (summation of t's)^2)
:
b = ((6 * 1205) - (13.5 * 480)) / ((6 * 34.75) - (13.5)^2)
:
b = 28.571428571 approx 28.57
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intercept(a) = (summation of the c's -(b*summation of t's)) / N
a = (480 - (28.57 * 13.5)) / 6
:
a = 15.7175 approx 15.72
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equation for c is
c(t) = 28.57x + 15.72
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