Chapter 5.3, Problem 27AYU

To determine

To find: The function is linear, exponential or neither.

Answer to Problem 27AYU

Solution:

Exponential function.

Explanation of Solution

Given:

x	-1	0	1	2	3
f ( x )	$\frac{1}{4}$	1	4	16	64

  

From the above table, the average rate of change from -1 to 0 is 0.75, and the average rate of change from 0 to 1 is 4. Because the average rate of change is not constant, the function is not a linear function. The ratio of consecutive output for a 1-unit increase in the input is a constant 4. Because the ratio of consecutive output from is constant, the function is an exponential function with growth factor $a=4$ . The initial value of the exponential function is $C=1.$ Therefore the exponential function that models the data is $H\left(x\right)= C{a}^x=4^x$ .