The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t2-.2672*t+14.8 where t is the year -1940. What is the expected MPG in 2025? How about 2050? Is this a valid function? Is there a top end to MPG?

Answer:

The equation is given as

MPG =0.0075 t2 - 0.2672 t + 14.8

Between 1940 and 2025, there are 85 years

Expected MPG in 2025 = 0.0075  852 - 0.2672  85 + 14.8

Expected MPG in 2025 = 46.28

Year 2050 corresponds to 110th year

Expected MPG in 2050 = 0.0075  1102 - 0.2672  110 + 14.8

Expected MPG in 2050 = 76.16

This is a valid function because due to improvment in technology and efficient engines, automobiles give more miles per gallon in future years compared to the present and previous year. The equation is a proof that automobiles in future give more miles per gallon.

There is no top end to MPG because as technology improves, automobiles in future can give more MPG and there is no limitation regarding maximum MPG.