The fuel efficiency (mpg rating) for cars has been increasing steadily since 1980. The formula for a car's fuel efficiency for a given year between 1980 and 1996 is E 0.36x + 15.9 where E is miles per gallon and z is the number of years after 1980. Note: Round your answers down to get the corresponding year. For instance, at 3.25, the year is 1983 .
a. In what years was the average fuel efficiency for cars less than 17 mpg (in interval form)?
b. In what years was the average fuel efficiency for cars more than 20 mpg (in interval form)?

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Joaobezerraid Joaobezerraid · Answer 1

Answer:

a) In the interval of [1980,1983].

b) In the interval of [1991, 1996].

Step-by-step explanation:

Fuel efficiency:

The fuel efficiency, for the cars, in x years after 1980, is given by:

[tex]E(x) = 0.36x + 15.9[/tex]

15.9 is the fuel efficiency in 1980.

a. In what years was the average fuel efficiency for cars less than 17 mpg (in interval form)?

From 1980 to:

[tex]E(x) < 17[/tex]

[tex]0.36x + 15.9 < 17[/tex]

[tex]0.36x < 1.1[/tex]

[tex]x < \frac{1.1}{0.36}[/tex]

[tex]x < 3.06[/tex]

3.06 = 1980 + 3 = 1983. So

In the interval of [1980,1983].

b. In what years was the average fuel efficiency for cars more than 20 mpg (in interval form)?

From x until 1996.

[tex]E(x) > 20[/tex]

[tex]0.36x + 15.9 > 20[/tex]

[tex]0.36x > 4.1[/tex]

[tex]x > \frac{4.1}{0.36}[/tex]

[tex]x > 11.38[/tex]

11.38 = 1980 + 11 = 1991. So

In the interval of [1991, 1996].