when the owner of a gas station sets the price of 1 gallon of unleaded gasoline at$4.10, he can sell approximately 1500 gallons per day. When he sets the price at $4.25 per gallon, he can sell approximately 1250 gallons per day. Let G(x) denote the number of gallons of unleaded gasoline sold per day when the price is x dollars. Assume that G(x) is a linear function of x. Approximately how many gallons will be sold per day if the price is set at $4.35 per gallon?

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12-09-2018
Mathematics

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when the owner of a gas station sets the price of 1 gallon of unleaded gasoline at$4.10, he can sell approximately 1500 gallons per day. When he sets the price at $4.25 per gallon, he can sell approximately 1250 gallons per day. Let G(x) denote the number of gallons of unleaded gasoline sold per day when the price is x dollars. Assume that G(x) is a linear function of x. Approximately how many gallons will be sold per day if the price is set at $4.35 per gallon?

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Riia Riia · Answer 1 · 2018-09-24T15:26:03+02:00

It is given in the question that

When the owner of a gas station sets the price of 1 gallon of unleaded gasoline at$4.10, he can sell approximately 1500 gallons per day. When he sets the price at $4.25 per gallon, he can sell approximately 1250 gallons per day. Let G(x) denote the number of gallons of unleaded gasoline sold per day when the price is x dollars.

First we put the given information in point form and find the slope ,m .

[tex]m = \frac{1250-1500}{4.25-4.10} = -1667[/tex]

Using point slope form, we will get

[tex]G(x) -1500 = -1667(x-4.10)[/tex]

[tex]G(x) = -1667x +8334.7[/tex]

When x = 4.35, we will get

[tex]G(x) = -1667(4.35)+8334.7 =1083.25[/tex]