Transportation The data below give the value of a used car over time. Which type of function best models the data? Write an equation to model the data.
Years | Value ($) |
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0 | 12,575 |
1 | 11,065 |
2 | 9750 |
3 | 8520 |
4 | 7540 |
5 | 6710 |
Know | Need | Plan |
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The value of a used car over time | The most appropriate model for the data | Graph the data and then use differences or ratios to find a model for the situation. |
Step 1 Graph the data.
The graph curves and does not look quadratic. It may be exponential.
Step 2 Test for a common ratio.
The value of the car is roughly 0.88 times its value the previous year.
Step 3 Write an exponential model.
Relate |
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Define | Let
Let |
Write |
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Step 4 Test two points other than (0, 12,575).
Test (2, 9750): | Test (4, 7540): |
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The point (2, 9738) is close to the data point (2, 9750). The point (4, 7541) is close to the data point (4, 7540). The equation
The table shows the annual income of a small theater company. Which type of function best models the data? Write an equation to model the data.
Year | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|
Income ($) | 18,254 | 18,730 | 19,215 | 19,695 | 20,175 |