what ios the average rate of change for this exponential function for the interval from x=2 to x=4
We cannot determine the average rate of change for an exponential function without knowing the specific function. Can you please provide the equation of the exponential function in question?
The curve begins close to X-axis at (minus 5.5, 0), rises at (minus 3, 0.1), passes through the closed points at (0, 1) on Y-axis, (1, 2), (2, 4), (3, 8), (5, 16) in quadrant 1.
Based on the points provided, it appears that the exponential function that represents the curve is of the form y = 2^x.
To find the average rate of change of this function on the interval from x = 2 to x = 4, we can calculate the rate of change between these two points.
At x = 2, y = 2^2 = 4
At x = 4, y = 2^4 = 16
The change in y over the interval from x = 2 to x = 4 is 16 - 4 = 12.
The change in x over the same interval is 4 - 2 = 2.
Therefore, the average rate of change between x = 2 and x = 4 is given by the change in y divided by the change in x:
Average Rate of Change = (16 - 4) / (4 - 2) = 12 / 2 = 6
So, the average rate of change for the exponential function y = 2^x on the interval from x = 2 to x = 4 is 6.