Here are the step-by-step workings to solve this problem:
The function given is: f(x) = 10(0.5)x
We are given 3 ordered pairs that the function passes through: (0,10), (1,5), and (2, 2.5)
We want to find the multiplicative rate of change of the function. This is how much the output changes for a one unit change in input.
When x increases from 0 to 1, f(x) decreases from 10 to 5. This is a decrease of 5.
When x increases from 1 to 2, f(x) decreases from 5 to 2.5. This is a decrease of 2.5.
Dividing the change in output (2.5) by the initial output (5) gives us the multiplicative rate of change: 2.5/5 = 0.5 or 50%.
Therefore, the multiplicative rate of change of the function is 50%.
The steps in summary are:
Find the change in output when x increases by 1
Divide this change by the initial output
This gives the multiplicative rate of change
In this case:
Change in output = 2.5
Initial output = 5
2.5 / 5 = 0.5 or 50%
So the multiplicative rate of change is 50%.
The key is calculating the change in output for a 1 unit change in input, and dividing that by the initial output. This gives the factor by which the output changes for each increment of the input.