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The curve through the ordered pairs (0, 10), (1, 5), and (2, 2. 5) can be represented by the function f(x) = 10(0. 5)x. What is the multiplicative rate of change of the function?.

User Malus Jan
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1 Answer

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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.

User Dgil
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