Question

Approximately how much greater is the estimated average rate of change of the function y=16⋅4x
over the interval [1.1,1.6]
than the estimated average rate of change of the function y=16x2+4x
over the same interval: 1, 10, or 100?(1 point)
The estimated average rate of change of the function y=16⋅4x
is approximately
greater than the estimated average rate of change of the function y=16x2+4x
over the interval [1.1,1.6]
.

Answer 1

Compute average rates of change:

For y = 16·4^x:
f(1.1) ≈ 16·4^1.1 ≈ 16·4.5948 = 73.52
f(1.6) ≈ 16·4^1.6 ≈ 16·9.184 = 146.94
AROC ≈ (146.94 − 73.52)/(1.6 − 1.1) ≈ 73.42/0.5 ≈ 146.85

For y = 16x^2 + 4x:
g(1.1) = 16(1.1)^2 + 4(1.1) = 23.76
g(1.6) = 16(1.6)^2 + 4(1.6) = 47.36
AROC ≈ (47.36 − 23.76)/0.5 = 23.6/0.5 = 47.2

Difference ≈ 146.85 − 47.2 ≈ 99.65 ≈ 100.

So the exponential’s average rate of change is approximately 100 greater.