What is the average rate of change formula for exponential growth functions?
if y = a e^kx
then
dy/dx = = k a e^kx = k y
if it is discrete
yn+1 = yn + k yn = (1+k) yn
hen
yn+1 - yn = k yn
in other words the change = constant times present value
The average rate of change (AROC) formula for exponential growth functions can be derived by taking the difference between the values of the function at two different points, and then dividing that difference by the corresponding change in the input values.
For an exponential growth function of the form f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth factor, the AROC between two points can be calculated using the following formula:
AROC = (f(x2) - f(x1)) / (x2 - x1)
In this formula, f(x2) represents the value of the function at the second point, f(x1) represents the value at the first point, x2 is the second input value, and x1 is the first input value.
To find the AROC, substitute the values of x2, f(x2), x1, and f(x1) into the formula and perform the calculations. The resulting value will represent the average rate of change between the two points on the exponential growth function.