Question

Compare the estimated average rate of change of the exponential function y=9(13)x
and the quadratic function y=9x2+13x
. Which function has a negative estimated average rate of change over the interval [0.1,0.6]
?(1 point)

both functions

neither function

the exponential function

the quadratic function

Answer 1

Neither function.

Both functions increase on [0.1, 0.6]. For example,
- Exponential: y(0.1) ≈ 9(13^0.1) ≈ 11.63, y(0.6) ≈ 9(13^0.6) ≈ 41.97, average rate ≈ (41.97−11.63)/0.5 ≈ 60.7 (positive).
- Quadratic: y(0.1) = 1.39, y(0.6) = 11.04, average rate = (11.04−1.39)/0.5 = 19.3 (positive).

So neither function has a negative average rate of change.