Answer:
Every time x increases by 1, y is multiplied by 0.5. That is the multiplicative rate of change.
Step-by-step explanation:
Well, I am not sure whether this is your question, but I kind of arranged the values into a more clear table.
x 1 2 3 4
y 0.25 0.125 0.0625 0.03125
To find the rate of change, you want to find what can be multiplied by the y-value to get another y-value as the x-value increases.
For example, you can see that when x is 1, y is 0.25. When x increases by 1, y is 0.125.
0.125 / 0.25 = 0.5. That means that when x increases by 1, y is multiplied by 0.5. You can check this by multiplying the rest of the values and seeing whether they match.
0.125 * 0.5 = 0.0625
0.0625 * 0.5 = 0.03125
Since the pattern continues, you can be sure that the multiplicative rate of change for y is 0.5.
The multiplicative rate of change of the exponential function is 0.5
From the table, we have the following representations
x 1 2 3 4
y 0.25 0.125 0.0625 0.03125
Divide yn by yn-1, to calculate the multiplicative rate (r) of change of the function
So, we have:
[tex]r = \frac{y_n}{y_{n - 1}}[/tex]
Let n = 2.
So, we have:
[tex]r = \frac{y_2}{y_{2 - 1}}[/tex]
This gives
[tex]r = \frac{y_2}{y_1}[/tex]
Substitute values for y2 and y1
[tex]r = \frac{0.125}{0.25}[/tex]
Divide
[tex]r = 0.5[/tex]
Hence, the multiplicative rate of change of the function is 0.5
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