Question

Billy is walking from the front door of his house to his bus stop, which is 940 feet away from his front door. As Billy walks out his front door he walks in a straight path toward his bus stop at a constant rate of 7.5 feet per second.

a) Define a function f to determine Billy's distance from his bus stop in terms of the number of seconds he has been walking.


b) What is the independent quantity and what is the domain of f (the values the independent quantity can take on)?


c) What is the dependent quantity and what is the range of f (the values the dependent quantity can take on)?


d) What do each of the following represent: f(0) and f(60.25)?


e) Use function notation to represent the following:
  i) Billy's distance from the bus stop after he has walked 23.6 seconds
  ii) The change in Billy's distance from the bus stop as the number of seconds since Billy left his front door increases from 25 seconds to 48 seconds

f) If t represents the number of seconds since Billy left his front door, solve f(t)=150 for t and say what your answer represents.

Answer 1

a) Let t represents the number of seconds he has been walking

b) The independent quantity is time in seconds and the domain of f varies from [0,infinity]

c) The dependent quantity is the distance in feet and the range varies from [0,infinity)

d) f(0) represents the distance moved is zero, which implies billy is standing at the front door

f(60.25) = 7.5(60.25) = 451.875 ft, which means billy has moved 451.875 ft from the front door

e) i) The function notation will be f(23.26)

ii) The change in distance will be given by f(48) - f(25)

f) f(t) = 150

7.5*t = 150

t = 20 seconds

Hence the number of seconds will be equal to 20

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