Question

Which function has the greater estimated average rate of change over the interval [0,1.1]
, the exponential function y=4x
or the quadratic function y=4x2
?

Option 1: exponential function

Option 2: quadratic function

(1 point)
The function with the greater estimated average rate of change on the interval is option
.

Answer 1

Compute the average rate of change = [f(1.1) − f(0)] / 1.1.

- Exponential y = 4^x: (4^{1.1} − 1)/1.1 ≈ (4.5948 − 1)/1.1 ≈ 3.5948/1.1 ≈ 3.269.
- Quadratic y = 4x^2: (4(1.1)^2 − 0)/1.1 = 4.84/1.1 = 4.4.

The quadratic function has the greater estimated average rate of change. Option 2.