Question

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)? all real numbers from 15 to 30 all real numbers from 0 to 30 all multiples of 5 from 0 to 30 all whole numbers from 0 to 15

Explanation:

Step1: Define the function

The fuel remaining \( F(h) \) can be modeled as a linear function. The initial fuel is 30 gallons, and it uses 5 gallons per hour. So, \( F(h)=30 - 5h \), where \( h \) is the number of hours ( \( 0\leq h\leq3 \) since the cruise is 3 hours).

Step2: Find the minimum and maximum of \( F(h) \)

• When \( h = 0 \) (start of the cruise), \( F(0)=30-5(0)=30 \) gallons.
• When \( h = 3 \) (end of the 3 - hour cruise), \( F(3)=30 - 5(3)=30 - 15 = 15 \) gallons.

Since \( h \) ranges from 0 to 3 (inclusive) and the function \( F(h)=30 - 5h \) is a linear function with a negative slope (so it is decreasing), the value of \( F(h) \) will range from 15 (when \( h = 3 \)) to 30 (when \( h = 0 \)). Also, since the fuel is consumed continuously (the boat uses fuel at a constant rate per hour, so the remaining fuel can take any real - number value in this interval), the range of \( F(h) \) is all real numbers from 15 to 30.

Answer:

all real numbers from 15 to 30