Questions: A person drives her car on a road trip. At the start of the trip, she fills up the 12.8-gallon tank with gasoline. During the trip, the car uses about 0.03 gallons of gasoline per mile. Let G be the number of gallons of gasoline remaining in the tank after driving d miles. The equation of a model to describe this situation is G=-0.03 d+12.8. Rewrite the equation G=-0.03 d+12.8 using the function name h. The equation G=-0.03 d+12.8 can be written with the function name h as . (Type an equation. Use integers or decimals for any numbers in the equation.)

A person drives her car on a road trip. At the start of the trip, she fills up the 12.8-gallon tank with gasoline. During the trip, the car uses about 0.03 gallons of gasoline per mile. Let G be the number of gallons of gasoline remaining in the tank after driving d miles. The equation of a model to describe this situation is G=-0.03 d+12.8. Rewrite the equation G=-0.03 d+12.8 using the function name h. The equation G=-0.03 d+12.8 can be written with the function name h as . (Type an equation. Use integers or decimals for any numbers in the equation.)
Transcript text: A person drives her car on a road trip. At the start of the trip, she fills up the 12.8 -gallon tank with gasoline. During the trip, the car uses about 0.03 gallons of gasoline per mile. Let G be the number of gallons of gasoline remaining in the tank after driving d miles. The equation of a model to describe this situation is $\mathrm{G}=-0.03 \mathrm{~d}+12.8$. Rewrite the equation $G=-0.03 d+12.8$ using the function name $h$. The equation $G=-0.03 \mathrm{~d}+12.8$ can be written with the function name $h$ as $\square$ . (Type an equation. Use integers or decimals for any numbers in the equation.)
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Solution

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Solution Steps

To rewrite the equation \( G = -0.03d + 12.8 \) using the function name \( h \), we simply replace \( G \) with \( h(d) \). This indicates that \( h \) is a function of \( d \), the number of miles driven. The equation becomes \( h(d) = -0.03d + 12.8 \).

Step 1: Define the Function

We start with the function that models the gallons of gasoline remaining in the tank after driving \( d \) miles, given by the equation: \[ h(d) = -0.03d + 12.8 \]

Step 2: Calculate Gallons Remaining

To find the number of gallons remaining after driving 100 miles, we substitute \( d = 100 \) into the function: \[ h(100) = -0.03(100) + 12.8 \]

Step 3: Perform the Calculation

Calculating the expression: \[ h(100) = -3 + 12.8 = 9.8 \]

Final Answer

The number of gallons remaining after driving 100 miles is \[ \boxed{9.8} \]

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