What is the estimated average rate of change of the function y = 16 x 4^x
The average rate of change of a function over a certain interval is equal to the change in the y-values divided by the change in the x-values.
For the function y = 16x * 4^x, we can calculate the average rate of change over an interval by evaluating the function at the two endpoints of the interval and finding the difference in the y-values, divided by the difference in the x-values.
Let's assume we are calculating the average rate of change over the interval [a, b]. The y-values at the endpoints are:
y(a) = 16a * 4^a
y(b) = 16b * 4^b
The difference in the y-values is:
y(b) - y(a) = 16b * 4^b - 16a * 4^a
The difference in the x-values is:
b - a
Therefore, the average rate of change over the interval [a, b] is:
(y(b) - y(a))/(b - a) = (16b * 4^b - 16a * 4^a)/(b - a)
Note that this formula gives you the average rate of change over a specific interval. If you want the average rate of change over the entire domain of the function, you would need to determine the endpoints of that domain.
Since you didn't specify an interval or domain, we cannot provide a specific numerical value for the estimated average rate of change.