calculate rate of change of function f(x) = (0.4)^x ;
x changes from x to x + 2.
kindly help in this
x = 0 and x = -2
rest i know how to solve
dont know the value of x
Huh? They give you the value of x. I read this as meaning when x=0
you want the average rate of change of f(x) between x=0 and x=2
f(x) = 0.4^x so
f(0) = 0.4^0 = 1
f(2) = 0.4^2 = 0.16
so the average rate of change is (0.16-1)/(2-0) = -0.42
That is the slope of the line from (0,1) to (2,0.16)
If I have it wrong, then please explain it further.
To calculate the rate of change of the function f(x) = (0.4)^x from x to x + 2, you need to find the difference in the function values at these two points divided by the difference in the x-values.
Step 1: Find f(x)
Let's substitute the given values of x, x = 0 and x = -2, into the function f(x) = (0.4)^x.
When x = 0:
f(0) = (0.4)^0 = 1
When x = -2:
f(-2) = (0.4)^(-2) = 1 / (0.4)^2 = 1 / 0.16 = 6.25
Step 2: Calculate the rate of change
Now, we can calculate the rate of change by finding the difference in the function values and dividing it by the difference in the x-values.
Rate of change = (f(x + 2) - f(x)) / (x + 2 - x)
Applying the values we found:
Rate of change = (f(0 + 2) - f(0)) / (2 - 0)
= (f(2) - 1) / 2
Now, you can substitute the value of x = 2 into the function to find f(2):
f(2) = (0.4)^2 = 0.16
Plugging this back into the rate of change equation:
Rate of change = (0.16 - 1) / 2
= -0.84 / 2
= -0.42
Therefore, the rate of change of the function f(x) = (0.4)^x, from x = 0 to x = 2, is -0.42.