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Concept explainers
(a)
The model that represents the data.
(a)
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Answer to Problem 26PT
There is a common ratio of 2, so the best model would be an exponential function to fit the data
Explanation of Solution
Given information:
CAR CLUB The table shows the number of car club members for four consecutive years after it began.
Time (years) | 0 | 1 | 2 | 3 | 4 |
Members | 10 | 20 | 40 | 80 | 160 |
Formula used:
Subtraction method is used.
Calculation:
First compare the first differences in the number of members:
Since they're not equal, compare the second differences:
Since the second differences are not equal, look for a common ratio:
There is a common ratio of 2, so the best model would be an exponential function to fit the data
Conclusion:
There is a common ratio of 2, so the best model would be an exponential function to fit the data
(b)
The function that models the data.
(b)
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Answer to Problem 26PT
The function that best fits the data is:
Explanation of Solution
Given information:
CAR CLUB The table shows the number of car club members for four consecutive years after it began.
Time (years) | 0 | 1 | 2 | 3 | 4 |
Members | 10 | 20 | 40 | 80 | 160 |
Formula used:
Calculation:
A function that fits the data should be an exponential function with a ratio of 2. The function of the form
The function that best fits the data is:
Conclusion:
The function that best fits the data is:
(c)
The car club members after 6 years.
(c)
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Answer to Problem 26PT
There will be 640 members after 6 years.
Explanation of Solution
Given information:
CAR CLUB The table shows the number of car club members for four consecutive years after it began.
Time (years) | 0 | 1 | 2 | 3 | 4 |
Members | 10 | 20 | 40 | 80 | 160 |
Formula used:
Substitution method is used.
Calculation:
To find the number of car club members after 6 years, use the function found in part b and plug in 6 for x.
There will be 640 members after 6 years.
Conclusion:
There will be 640 members after 6 years.
Chapter 9 Solutions
Algebra 1, Homework Practice Workbook (MERRILL ALGEBRA 1)
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