Chapter Test
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Use the graph to make a table of points. Find how the y-values change with each x-value.
Type of Function: Exponential
Equation: y=40( 12)^x
First let's identify if the graph is linear, quadratic, or exponential. We will make a table of points from the graph.
| x | y |
|---|---|
| 0 | 40 |
| 1 | 20 |
| 2 | 10 |
| 3 | 5 |
Now to determine what kind of function this is, let's look at how the y-value changes each time.
Alternatively, we can see that this function is exponential by looking at the graph. The graph is not a line, so the function is not linear. Similarly, the graph does not appear to be a parabola, so the function is not quadratic.
Now we will write an equation for this exponential function. Let's use the general model for exponential functions. y=ab^x In the equation a is the initial value. That is, it is the y-value when x=0. We can see from our table and graph that when x=0, y=40. y=40b^x Now, let's find the b-value, which represents the decay factor. In our scenario, we can see that each y-value gets cut in half. This tells us that the decay factor is 12. y=40(1/2)^x We now have an equation that models the data.