Does the function represent exponential growth or exponential decay. Identify the growth or decay factor. y=9 x (1/2)
I'm not sure how to make the chart to show the decay.
If you mean y = 9x1/2 it is not even exponential. An exponential function has x in the exponent, such as
y = 9 * (1/2)^x
which would be decay, because powers of fractions get progressively smaller.
If you don't know how to even make a chart, you are in trouble. For a chart, just pick values of x and evaluate the corresponding y. Then, uh, put them in the chart!
The function y = 9 * (1/2) represents exponential decay.
To create a chart showing the decay, you can choose different values for x and calculate the corresponding y values.
Here, let's choose some values for x and calculate the corresponding y values:
x = 0, y = 9 * (1/2)^0 = 9 * 1 = 9
x = 1, y = 9 * (1/2)^1 = 9 * 1/2 = 4.5
x = 2, y = 9 * (1/2)^2 = 9 * 1/4 = 2.25
x = 3, y = 9 * (1/2)^3 = 9 * 1/8 = 1.125
x = 4, y = 9 * (1/2)^4 = 9 * 1/16 = 0.5625
Plotting these values on a chart, you will see that as x increases, the corresponding y values decrease exponentially.
To determine if a function represents exponential growth or decay, we need to analyze the base of the exponent.
In the given function, the base is 1/2, which is less than 1. When the base is less than 1, it represents exponential decay. On the other hand, if the base is greater than 1, it represents exponential growth.
Now, let's find the growth or decay factor for this function. The growth or decay factor is simply the base of the exponential function. In this case, the factor is 1/2.
To create a chart representing the decay, you can choose some values for x and calculate the corresponding y values.
Here's an example of a chart:
| x | y |
|-------|-------|
| 0 | 9 |
| 1 | 4.5 |
| 2 | 2.25 |
| 3 | 1.125 |
| 4 | 0.5625|
In this chart, as x increases by 1, we can see that the y values decrease by a factor of 1/2, which demonstrates the exponential decay.
I hope this explanation helps you understand how to determine if a function represents exponential growth or decay and how to create a chart to show the decay.