Chapter 5.3, Problem 29AYU

To determine

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

Answer to Problem 29AYU

Solution:

Exponential function .

Explanation of Solution

Given:

x	-1	0	1	2	3
f ( x )	$\frac{3}{2}$	3	6	12	24

  

From the above table, the average rate of change from -1 to 0 is 1.5, and the average rate of change from 0 to 1 is 3. 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 2. Because the ratio of consecutive output from is constant, the function is an exponential function with growth factor $a=2$ . The initial value of the exponential function is $C=3.$ Therefore the exponential function that models the data is $F\left(x\right)= C{a}^x=3{\left(2\right)}^x$ .