Question

The distance from city A to city B is approximately 2160 miles. A plane flying directly to city B passes over city A at noon. If the plane travels at 480 mph, find the rule of the function​ f(t) that gives the distance of the plane from city B at time t hours​ (with t=0 corresponding to​ noon).

​f(t)=

Answer 1

City: Source------------------A------------------- B

Dist: Source------------------A--------2160---- B

Time:Source-----------------12----------------- B (real time)

t: Source------------------0---------------------- B (function time)

Notice that distance between A and B is 2160.

so at t = 0, the distance of the plane from city B is 2160.

Speed of the plane if 480 mph, so every hour the plane travels 480 miles. (y-intercept)

Which means the distance between plane and city B is reducing by 480 miles every hour.

So this is rate of change of distance, which is called slope of the line. Slope = -480

so distance between plane and city (d) = 2160 - 480t

so answer is 2160 - 480t