Concept explainers
a.
The zeroes of the given function
a.
Answer to Problem 44PPS
The zero of the given function is 8.
Explanation of Solution
Given:
Where,
p is the percents of process left to complete.
t is the time in minutes that the solution is left on the hair.
Calculation:
In order to find the zero of the function, put p = 0.
Conclusion:
Hence, the zero of the function is 8.
b.
To plot the graph of the situation.
b.
Explanation of Solution
Given:
Calculation of graph:
Consider,
Values of t | Values of f ( t ) |
0 | 100 |
1 | 87.5 |
2 | 75 |
3 | 62.5 |
8 | 0 |
Using the above table, the graph can be plotted.
Graph:
Interpretation:
x- intercept: The graph intersects the x -axis at about (8,0), hence the x- intercept will be 8. This means in 8 minutes the whole process will be completed.
y- intercept: The graph intersects the y -axis at about (0,100), hence the y- intercept will be 100. This means that initially no percentage of the process is completed..
Conclusion:
Hence, the graph obtained is a line.
c.
To explain what the zero represents.
c.
Explanation of Solution
Given:
Where,
p is the percents of process left to complete.
t is the time in minutes that the solution is left on the hair.
Calculation:
In order to find the zero of the function, put p = 0.
So, at t = 8 minutes, p = 0%, which means the whole process is completed by this time.
d.
To state the domain and range of this function.
d.
Answer to Problem 44PPS
Domain:
Range:
Explanation of Solution
Given:
Where,
p is the percents of process left to complete.
t is the time in minutes that the solution is left on the hair.
Since the t represents time, it will start with 0 minutes and go until 8 minutes (which is the zero of the function) and beyond that the value of p will become negative which is not possible because p represents the percentage which will lie in
Hence,
Domain:
Range:
The above statement can be verified with the graph also.
Calculation of graph:
Consider,
Values of t | Values of f(t) |
0 | 100 |
1 | 87.5 |
2 | 75 |
3 | 62.5 |
8 | 0 |
Using the above table the graph can be plotted.
Graph:
Interpretation:
x- intercept: The graph intersects the x -axis at about (8,0), hence the x- intercept will be 8. This means in 8 minutes the whole process will be completed.
y- intercept: The graph intersects the y -axis at about (0,100), hence the y- intercept will be 100. This means that initially no percentage of the process is completed..
Conclusion:
Hence from the statement and graph it can be concluded that:
Domain:
Range:
Chapter 3 Solutions
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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