An approximate linear model that gives the remaining distance, in miles, a plane

Question

An approximate linear model that gives the remaining distance, in miles, a plane must travel from Los to Angles to Boston is given by s(t) = 9000 - 600t where s(t) is the remaining distance t hours after the flight begins. (a) Find the vertical and horizontal intercepts of s(t). (b) Explain (using sentences) what the horizontal and vertical intercepts of s(t) represent in the context of this problem. (You should have one sentence for each intercept.) (c) Find the slope of s(t). (d) Explain (using an English sentence) what the slope of s(t) represents in the context of this problem.

Explanation / Answer

(a) s(t) = 9000 - 6000t

Horizontal intercept is at s(t) = 0

=> 9000 - 600t = 0

=> t = 9000/600

=> t = 15 hours

Vertical intercept is at t = 0

=> s(0) = 9000 - 0 = 9000 miles

(b) The horizontal intercept is the time taken to cover the distance from Los Angeles to Boston.

The vertical intercept is the distance from Los Angeles to Boston.

(c) The slope of s(t) is s'(t)

Differentiating s(t)

s'(t) = -6000

(d) The slope of s(t) represents the instantaneous velocity t hours after the flight begins.

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