A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees

Question

Fahrenheit, for those months. The scatter plot shows the data. The function  best fits these data. 

Graph- (60,25), (40,40),(40,45),(20,55),(10,60)

Use the function  to determine which of the following statements are true. Select all that apply.

A- The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

B- The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.

C- The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.

D- The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

E- The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

 

Answer 1

The function is:

A(t) = -1.4t + 96

Where A(t) is the amount of oil used and t is the temperature.

A) This question says that A(t) should equal 82 when t = 10. Let's see if it's true. Let's plug t = 10 into the A(t) function and see if it equals 82:

A(t) = -1.4t + 96

A(t) = -1.4·10 + 96

A(t) = -14 + 96

A(t) = 82 gallons

So yes, question (A) is true. All of the rest of the problems (B through E) work the same way. Just plug the value of t that they give you into the function and see if gives you the number of gallons stated in the problem. If it does, it's true. If it doesn't, it's false.