Question

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?

Answer 1

To find the number of gallons that will be sold per day when the price is set at $4.35 per gallon, you can use the given information to calculate the linear function for the number of gallons sold. By finding the slope and y-intercept, you can substitute the price of $4.35 into the function to determine the approximate number of gallons sold per day.

Step-by-step explanation:

To find the number of gallons that will be sold per day when the price is set at $4.35 per gallon, we can use the information provided about the relationship between price and quantity sold.

First, let's calculate the slope of the linear function. The change in quantity is 1500 - 1250 = 250 gallons. The change in price is $4.10 - $4.25 = -$0.15. So the slope is -250 / -0.15 = 1666.67 gallons per dollar.

Next, we can use the slope-intercept form of a linear function, y = mx + b, where y represents the number of gallons sold, x represents the price in dollars, m represents the slope, and b represents the y-intercept. Using the given points (4.10, 1500) and (4.25, 1250), we can solve for b. Plugging in the values, we get 1500 = 1666.67(4.10) + b. Solving for b, we find that b = -2148.67. Therefore, the linear function for the number of gallons sold, G(x), is G(x) = 1666.67x - 2148.67.

Finally, we can substitute x = 4.35 into the equation to find the number of gallons sold per day. G(4.35) = 1666.67(4.35) - 2148.67 = 4083.335 gallons (approximately).

Answer 2

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 .

`m = (1250-1500)/(4.25-4.10) = -1667`

Using point slope form, we will get

`G(x) -1500 = -1667(x-4.10)`

`G(x) = -1667x +8334.7`

When x = 4.35, we will get

`G(x) = -1667(4.35)+8334.7 =1083.25`