Question

Jim purchased a fuel-efficient hybrid car that gets 50 miles per gallon.

a. If the fuel tank in Jim's car holds 13 gallons of fuel, define a formula to determine the number of gallons of fuel in Jim's fuel tank, n, in terms of the number of miles z that Jim has driven since filling his tank.

Answer 1

We want to write a linear function that models the given situation, where a linear function is written as:

$y = a*x +b$

where a is the slope and b is the y-intercept.

The function will be:

$T(z) = (-0.02 gal/mi)*z + 13 gal.$

The information that we have here is:

The car gets 50 miles per gallon.

The tank holds 13 gallons of fuel.

We want to write a function that gives the number of gallons in the tank as a function of the miles driven.

Let's define the variable:

z = number of miles

Then the function T(z) will give us the number of gallons in the tank as a function of z.

$T(z) = a*z + b$

We know that if there are no miles driven (z = 0), then the tank should be full, so we have:

$T(0 mi) = 13 gal = a*0mi + b\\\\ 13 gal = b$

Then we found the value of b, and the function becomes

$T(z) = a*z + 13 gal.$

Now we know that for every 50 miles driven, the car uses one gallon.

Then the rate (or slope) at which the fuel is consumed is:

$a = -(1 gallon)/(50 miles) = -0.02 gal/mi$

Where the negative sign is because the fuel is being consumed.

We can replace that in the function to get:

$T(z) = (-0.02 gal/mi)*z + 13 gal.$

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