Please help me!!!!?

Question

(not a linear equation) Math problem: An automotive engineer studied the effect of car weight in tons on fuel efficiency, which is measured in miles per gallon (mpg). The data from two cars in the study showed that a 2 ton car had a fuel efficiency of 35 mpg and a 2.5 ton car had a fuel efficiency of 31 mpg. Find a linear model that gives the fuel efficiency E (in mpg) of a car as a function of its weight w (in tons).

E =

Use the model to find the fuel efficiency (in mpg) of a car that weighs 3 tons.

mpg

E =

Use the model to find the fuel efficiency (in mpg) of a car that weighs 3 tons.

mpg

Ian H · Accepted Answer

Find a linear model  ..............
E = mW + c
35 = 2m + c
31 = 2.5m + c
4 = -0.5m
 m = -8
35 = -16 + c
c = 51
E = -8W + 51 and if W = 3 tons
E = -8*3 + 51 = 27 mpg

but y = 40/x + 15 by billrussell is good if non linear wanted

billrussell42 · Answer

umm, first you say "not a linear equation" then you ask for a linear model....

data points: 2 ton and 35 mpg
                   2.5 ton and 31 mpg

I'd use y (mpg) = a/x + b
     where x is tons

plug in the points and get a and b
35 = a/2 + b
31 = a/2.5 + b

70 = a + 2b
77.5 = a + 2.5b

a = 70 – 2b = 77.5 – 2.5b
2.5b – 2b = 77.5 – 70
0.5b = 7.5
b = 15
a = 70 – 30 = 40

so eq is
y = 40/x + 15

check
x = 2, y = 20+15 = 35
x = 2.5, y = 16+15 = 31

x = 3, y = 40/3 + 15 = 28.3 mpg

Please help me!!!!?

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