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)

the exponential function

neither function

the quadratic function

both functions

Answer 1

Average rate of change = [y(0.6) − y(0.1)] / (0.6 − 0.1).

Exponential y = 9·13^x:
y(0.6) ≈ 9·13^0.6 ≈ 9·4.66 ≈ 41.94
y(0.1) ≈ 9·13^0.1 ≈ 9·1.292 ≈ 11.63
Average rate ≈ (41.94 − 11.63)/0.5 ≈ 60.62 (positive)

Quadratic y = 9x^2 + 13x:
y(0.6) = 9(0.6)^2 + 13(0.6) = 3.24 + 7.8 = 11.04
y(0.1) = 9(0.1)^2 + 13(0.1) = 0.09 + 1.3 = 1.39
Average rate = (11.04 − 1.39)/0.5 = 19.3 (positive)

Neither function has a negative average rate of change.