To graph the function, make a table of values first.
Type of Function: Exponential decay. Percent decrease: 66.7 % Graph:
Practice makes perfect
We will tell whether the function represents exponential growth or exponential decay, identify the percent increase or decrease, and graph the function, one at a time
Exponential Growth or Exponential Decay?
Let's start by identifying the value of the base of the exponential function.
f(x)=( 13 )^x
Because the base of the function is greater than 0, but less than 1, we know that this is an exponential decay function.
Percent Increase or Decrease
To identify the percent decrease, we will first analyze the exponential decay model.
Exponential Decay Model
y=a(1-r)^t
In the model, a is the initial amount and r is the percent decrease written as a decimal. Knowing that the base of the function is 13, we can identify the annual percent decrease.
Therefore, the annual percent decrease is approximately 66.7 %.
Graphing the Function
To draw the graph, we will start by making a table of values.
x
(1/3)^x
f(x)=(1/3)^x
- 3
(1/3)^(- 3)
27
- 2
(1/3)^(- 2)
9
- 1
(1/3)^(- 1)
3
0
(1/3)^0
1
1
(1/3)^1
1/3
2
(1/3)^2
1/9
The ordered pairs ( - 3, 27), ( - 2, 9), ( - 1, 3), ( 0, 1), ( 1, 13), and ( 2, 19) all lie on the graph of the function. Now, we will plot and connect these points with a smooth curve.
