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.
x f(x)
-1 8/7
0 8
1 56
2 392

Answer 1

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 \(\displaystyle{y}={a}{b}^{{x}}\)
where a is the initial value (where x= 0) and & is the common ratio. Substitute a = 8 and b= 7 so: \(\displaystyle{y}={8}{\left({7}\right)}^{{x}}\)
or
\(\displaystyle{f{{\left({x}\right)}}}={8}{\left({7}\right)}^{{x}}\)