When asked to determine the rate of change from the first point to the second point - `x_(2) = 3 and x_(2) = 4` for the function, `y = 2^x` , will we perform the same operation as usual? Note how we have two points "considered" the same, but have different values (`x_(2) and x_(2), 3 and 4` ).

Would the following solution to this be incorrect?

Average rate = `[f(x_(2)) - f(x_(2))]/(x_(2)-x_(2)) = (16 - 8)/(4-3) = (8/1) = 8`

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I suspect strongly that your problem set has a typographical error. First, there is no rate of change moving from a point to itself. Second, a function cannot have two different output values for the same input value.

Considering the problem as determine the rate of change from `x_1=3` to `x_2=4` we would get:

`((f(x_2)-f(x_1))/(x_2-x_1)=(2^4-2^3)/(4-3)=8`

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Yes I figured it must be a typo; however, I just wanted to receive clarification in order to be certain of my assumption. Thank you.

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