Chapter 6.2, Problem 38E

To determine

To find: whether thefunction that is represented by the table is exponential growth function, exponential decay function or neither.

Answer to Problem 38E

Exponential Decay Function

Explanation of Solution

Given information:

The table:

x	3	5	7	9
y	432	72	12	2

Concept Used:

Exponential growth function:

  $y=a{\left(1+r\right)}^t$

Here, the y is the final value, a is the initial value, and r is the rate of growth (in decimal form).

Exponential decay function:

  $y=a{\left(1-r\right)}^t$

Here, the y is the final value, a is the initial value, and r is the rate of decay (in decimal form).

Consider the table given below:

  

It can be observed that as x increases by 2, the value of yis multiplied by $\frac{1}{6}$ .

So, the function represented by the given table is exponential decay function.