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Summarize how to determine whether a given set of data is modeled by a linear function, a quadratic function, or an exponential function.
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Explanation of Solution
Concept used:
- If the first differences are constant for any set of data, then it is modeled by a linear function.
- If first differences are not constant but the second differences are constant, then data is modeled by a quadratic function.
- If the ratios are constant, then the data can be modeled by an exponential function.
Calculation:
The best way to determine whether the given data represents a linear function, a quadratic function or an exponential function, one can graph and identify it easily.
If the graph is a straight line, then the data is modeled by a linear function. And if the graph is a parabola, then the data will be modeled by a quadratic function. Otherwise if the function is keep increasing or decreasing from left to right in the form of a curve, then it will represent an exponential function.
In other way, one can determine whether the given set of data modeled by a linear, a quadratic or an exponential function by finding the differences of y -values. If the differences of y -values of the data set are constant, then the data can be modeled by a linear function.
And if the first differences are not equal, but the second differences are equal, then the data can be modeled by a quadratic function.
And if the ratios of the y -values are constant, then the data can be modeled by an exponential function.
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