How do I solve this?

Question

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 year -1940.

Answer the following questions:

1. What is the expected MPG in 2025?
2. How about 2050?
3. Is this a valid function?
4. Is there a top end to MPG?

Answer 1

f(t) = 0.0075t² - 0.2672t + 14.8

Expected MPG in 2025: f(2025 - 1940) = f(85) = 0.0075(85)² - 0.2672(85) + 14.8 = 46.2755

Expected MPG in 2050: f(2050 - 1940) = f(110) = 0.0075(110)² - 0.2672(110) + 14.8 = 76.158

Is this a valid function? Yes, for every input value there is only one output value. If you plot the function, you can also verify function validity with the vertical line test.

Is there a top end to MPG? No, the second-order polynomial has a positive leading coefficient. This information tells us that the graph of the function is an upwards U shape that increases to infinity as t increases.