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Explain how to determine whether a set of data displays exponential behavior.
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Explanation of Solution
Given:
Explain how to determine whether a set of data displays exponential behavior.
Concept Used:
Exponential equations of the form:
Using Differences to Determine the Model By finding the differences between dependent values, you can determine the degree of the model for data given as ordered pairs.
- If the first difference is the same value, the model will be linear.
- If the second difference is the same value, the model will be quadratic.
- If the number of times the difference has been taken before finding repeated values exceeds five, the model may be exponential or some other special equation.
By taking the ratio of the values, one can determine whether the model is exponential.
If the ratio of dependent values is the same, then the data is modeled by an exponential equation.
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