Question

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Using the exponential function 2x + 3, what is the average rate of change between the values 1 ≤ x ≤ 5?


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Answer 1

7.5

Explanation:

The given exponential function is

`f(x) = {2}^(x) + 3`

The average rate of change over a≤x≤b is given by;

`(f(b) - f(a))/(b - a)`

This implies that the average rate of change between the values 1 ≤ x ≤ 5 is

`(f(5) - f(1))/(5 - 1)`

We evaluate to get:

`\frac{ {2}^(5) + 3 - {2}^(1) - 3}{4} = (30)/(4) = (15)/(2) = 7.5`