Fall 2005 #31 linear interpolations??

[mlt32]

piecewise with endpoints (0,1) (25,.5) (75, 0.40) (100,0)

find (20p15*35q35) / 55q35?

solutions just says S(15) = .7..ok I get that
S(35) = .48...not getting...help please

[jplank1983]

75 - 25 = 50

35 is 10 units away from 25 and 40 units away from 75. So, linear interpolation is:

S(35) = (10/50)*0.4 + (40/50)*0.5 = 0.48

[Actuarialsuck]

If you don't want to think about it that way, you should remember the formula from Algebra 1 for fiding a line given 2 points.

x = 35 is between x = 25 and x = 75 based on your data points so your two points of interest are (25, .5) and (75, .4). The slope is (.4 - .5) / (75 - 25) = -.002 and the formula for a line is y - y1 = m(x-x1) i.e. y = -.002(x - 25) + .5. Since x = 35 you can plug it in to get y = -.002(35 - 25) + .5 = .48

[mlt32]

got it, thanks for the quick reply...brain on overload, can't remember the simple stuff plus college algebra was over 20 years ago!