Answer:
The average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear.
Step-by-step explanation:
See the table attached.
The average rate of change on [1,3] is = [tex]\frac{32 - 8}{3 - 1} = 12[/tex]
The average rate of change on [2,4] is = [tex]\frac{64 - 16}{4 - 2} = 24[/tex]
Again, the average rate of change on [1,5] is = [tex]\frac{128 - 8}{5 - 1} = 30[/tex]
Therefore, the average rate of change on [1,3] is [tex]\frac{1}{2}[/tex] the average rate of change on [2,4]. The average rate of change on [1,3] is [tex]\frac{2}{5}[/tex] the average rate of change on [1,5]. So the function can not be linear. (Answer)
