From the table below, determine whether the data shows an exponential function. Explain why or why not. x –5 –4 –3 –2 y 0.5 2 8 32

The x-values increase by 1 each time, so they are at regular intervals. For each increase of 1 in x, the y-value is multiplied by 4: 2 ÷ 0.5 = 4, 8 ÷ 2 = 4, and 32 ÷ 8 = 4. Therefore, the data show an exponential function, and the best answer is “Yes; the domain values are at regular intervals and the range values have a common factor 4.”

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