Question

A jetliner uses 3,600 gallons of fuel per hour while it is cruising, and there are 15,000 gallons of fuel in the jetliner's fuel tank when it begins to cruise. If y represents the amount of fuel, in thousands of gallons, remaining in the fuel tank after the jetliner cruises for x hours. What is the graph of the solution set for this, and the equation modeled by the graph??

a) Graph: Exponential decay, Equation: y=15−3.6x

b) Graph: Linear, Equation: y=15−3.6x

c) Graph: Exponential growth, Equation: y=15+3.6x

d) Graph: Linear, Equation: y=15+3.6x

Answer 1

The jetliner's fuel consumption over time is modeled by a linear graph and the equation y = 15 - 3.6x, representing a straight line that slopes downward, indicating a decrease in fuel as time increases.

Step-by-step explanation:

The question is asking to determine the type of graph and the equation that models the amount of fuel left in a jetliner's tank as it cruises over time, with a starting amount of 15,000 gallons and a consumption rate of 3,600 gallons per hour. The correct choice is a linear equation and graph, as the amount of fuel decreases at a constant rate as time passes. There is no compounding effect that would cause the relationship between the hours flown and fuel remaining to be exponential.

The correct equation is y = 15 - 3.6x "with y" representing the amount of fuel remaining in thousands of gallons after "x hours" of cruising. Every hour, the jet uses 3.6 thousand gallons of fuel, which is subtracted from the initial 15 thousand gallons. Hence, the graph that models the solution is a straight line that slopes downward, indicating a decrease in fuel over time