Question

The Beechcraft 1900D is a commuter airplane with a fuel capacity of 665 gallons. The function that represents how the amount of fuel changes as a function of distance flown is f(x)=−0.9x+665, where x represents miles flown, and f(x) represents the amount of fuel remaining. What is the rate of change for this scenario?

Answer 1

Given:

The  function that represents how the amount of fuel changes as a function of distance flown is

$f(x)=-0.9x+665$

where x represents miles flown, and f(x) represents the amount of fuel remaining.

To find:

The rate of change for this scenario.

Solution:

The slope intercept form of a linear function is

$y=mx+b$        ...(i)

Where, m is the slope or rate of change and b is the y-intercept.

We have,

$f(x)=-0.9x+665$        ...(ii)

On comparing (i) and (ii), we get

$m=-0.9$

Therefore, the rate of change for this scenario is -0.9. It means, the amount of fuel in the airplane is decreasing by 0.9 gallons per mile.