Concept explainers
(a)
Forming table, graph and equation.
(a)
Explanation of Solution
Given data:
Starting with 128 teams half of the remaining team eliminated each round.
Formula used:
An exponential decay function is
a is initial value
b is growth rate
Calculation:
Initial number of team is 128
As every time half team eliminated so growth factor is
So the function is
x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
y | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Conclusion:
Its an exponential graph.
(b)
Is it possible to remain 24 teams after a round.
(b)
Answer to Problem 32PPE
No it is not possible
Explanation of Solution
Given data:
Calculation:
No it is not possible as by the graph in part (a) it can be seen that there is no value which is equal to 24 on the integer.So graph is the easiest way to represent the situation.
Conclusion:
No it is not possible
(c)
Domain of the function.
(c)
Answer to Problem 32PPE
The domain of the function is
Explanation of Solution
Given data:
Calculation:
By the table in part (a) the starting value was 0 as first round than second round started which is x=1 and than third round is x=2 and at x=7 there is only 1 team left
So the domain of the function is
The domain of function represent the number of team left after each round.
Conclusion:
The domain of the function is
(d)
Number of team left after 5 rounds.
(d)
Answer to Problem 32PPE
4 teams were left after 5 rounds.
Explanation of Solution
Given data:
5 rounds were completed.
Formula used:
Calculation:
Number of teams after 5 rounds:
Conclusion:
4 teams were left after 5 rounds.
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