Chapter 6, Problem 14CR

To determine

whether the function that is represented by the table is exponential growth function, exponential decay function or neither:

x	1	2	3	4
y	162	108	72	48

Answer to Problem 14CR

Exponential Decay Function

Explanation of Solution

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 1, the value of y is multiplied by $\frac{2}{3}$ .

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