Determine whether the function given by the table is linear, exponential, or nei

Question

Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data; if it is exponential, find an exponential function that models the data. Select the correct choice below and fill in any answer boxes within your choice. The function is exponential An exponential function that models the data is . (Simplify your answer.) The function is linear. A linear function that models the data is . (Simplify your answer.) The function is neither linear nor exponential.

Explanation / Answer

If the function is linear, it would fit f(x) = ax + b.
Fitting in (0,1) and (1,5), we get b = 1 and a = 4.
However, if we plug in x = 2, we don't get f(x) = 25. We get f(x) = 9, which means the function isn't linear.

If the function is exponential, it would fit f(x) = a*bx.

Fitting in (0,1) and (1,5), we get a = 1 and b = 5.

This fits the rest of the data, so the answer is A, and f(x) = 5x.

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