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

Question
Asked Sep 23, 2019
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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 ff (the values the independent quantity can take on)?


c) What is the dependent quantity and what is the range of ff (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.

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Expert Answer

Step 1

Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If you want remaining sub-parts to be solved, then please resubmit the whole question and specify those sub-parts you want us to solve.

Now, come to the question:

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

s 940 feet and v = 7.5 feet/sec
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s 940 feet and v = 7.5 feet/sec

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Step 2

Now, the initial velocity of the Billy’s is zero that is u=0 feet/sec. then distance S can be calculated as:

1
s ut at
2
1
a =
2
1
2t
1
s v
2
v7.5 feet/sec)
1
(7.5)t
2
s 3.75t feet
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1 s ut at 2 1 a = 2 1 2t 1 s v 2 v7.5 feet/sec) 1 (7.5)t 2 s 3.75t feet

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Step 3

The distance function f(s) in te...

ft)3.75tf()= s)
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ft)3.75tf()= s)

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