Question

Find the average rate of change of 𝑓⁡(𝑥) =𝑒𝑥−1 +3 over the interval [1,5]. Round your answer to the nearest tenth.

Answer 1

I’m not sure how to parse f(x) from your text — it could be one of these common meanings:

1) f(x) = e^(x−1) + 3
2) f(x) = e^x − 1 + 3 = e^x + 2
3) f(x) = e·x − 1 + 3 = e x + 2

Here are the average rates of change on [1,5] for each:

- If f(x) = e^(x−1) + 3:
(f(5) − f(1)) / 4 = (e^4 + 3 − 4) / 4 = (e^4 − 1)/4 ≈ 13.4

- If f(x) = e^x + 2:
(f(5) − f(1)) / 4 = (e^5 + 2 − (e + 2)) / 4 = (e^5 − e)/4 ≈ 36.4

- If f(x) = e x + 2 (linear with slope e):
Average rate of change = slope = e ≈ 2.7

Which version of f(x) did you mean?