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)
Responses

the quadratic function
the quadratic function

the exponential function
the exponential function

both functions
both functions

neither function
neither function

Answer 1

Neither function.

Reason: AROC = (y(0.6) − y(0.1))/0.5.

- Quadratic: y(0.6)=9(0.6)^2+13(0.6)=11.04, y(0.1)=9(0.1)^2+13(0.1)=1.39 → AROC = (11.04−1.39)/0.5 = 19.3 (>0).

- Exponential: y=9·13^x gives y(0.6)≈41.95, y(0.1)≈11.63 → AROC ≈ (41.95−11.63)/0.5 ≈ 60.64 (>0).

Both average rates are positive, so neither is negative.