# Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models th

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. x f(x) -1 8/7 0 8 1 56 2 392
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The function is linear if there is a common difference between the y-values for a constant increase in the z-values while the function is exponential if there is a common ratio between the y-values for a constant increase in the z-values.
Since there is a common ratio of 7 between the y-values for « constant increase of 1 in the x-values, then the function is exponential.
Use the exponential model $y=a{b}^{x}$
where a is the initial value (where x= 0) and & is the common ratio. Substitute a = 8 and b= 7 so: $y=8{\left(7\right)}^{x}$
or
$f\left(x\right)=8{\left(7\right)}^{x}$