College

Lindsey is the captain of a pontoon boat. This weekend, she is taking a birthday party out for a 3-hour boat cruise. The boat's gas tank holds 30 gallons of fuel when the cruise begins, and it uses 5 gallons per hour at cruising speed.

The function \( F(h) \) represents the volume of fuel, in gallons, remaining in the boat's gas tank after \( h \) hours of the cruise.

What is the range of \( F(h) \)?

Answer :

Final answer:

The range of the function F(h) representing the fuel remaining after h hours in a boat's gas tank is from 15 to 30 gallons.

Explanation:

The student asked about the range of the function F(h), which represents the volume of fuel remaining in the boat's gas tank after h hours of a cruise.

Given that the boat starts with 30 gallons of fuel and uses 5 gallons per hour, we can establish the equation

F(h) = 30 - 5h. During a 3-hour cruise, the function ranges from the initial amount of fuel to the amount remaining after 3 hours: F(0) = 30 gallons and F(3) = 30 - (5*3) = 15 gallons.

Thus, the range of F(h) is the set of values that F(h) can take, which is from 15 to 30 gallons.