What is the average rate of change of the function f(x)=20(1/4)^x from x = 1 to x = 2?
Enter your answer as a decimal. Do not round.
it is the slope of the line joining (1,f(1)) and (2,f(2)):
(1,20/4) and (2,20/16)
(20/16 - 20/4)/(2-1) = ?
30?
To find the average rate of change of a function from x = a to x = b, you can use the formula:
Average rate of change = (f(b) - f(a)) / (b - a)
For the given function, f(x) = 20(1/4)^x, we need to find the value of f(1) and f(2) and substitute them into the formula.
f(1) = 20(1/4)^1 = 5
f(2) = 20(1/4)^2 = 1.25
Using the formula, we have:
Average rate of change = (f(2) - f(1)) / (2 - 1)
= (1.25 - 5) / (2 - 1)
= -3.75
Therefore, the average rate of change of the function f(x)=20(1/4)^x from x = 1 to x = 2 is -3.75.
To find the average rate of change of a function from x = 1 to x = 2, we need to calculate the difference in the function values at these two points and divide it by the difference in the x-values.
Given the function f(x) = 20(1/4)^x, we need to find the difference in the function values at x = 1 and x = 2.
Step 1: Calculate the function value at x = 1.
Substitute x = 1 into the function to get:
f(1) = 20(1/4)^1 = 20(1/4) = 20/4 = 5.
Step 2: Calculate the function value at x = 2.
Substitute x = 2 into the function to get:
f(2) = 20(1/4)^2 = 20(1/16) = 20/16 = 5/4 = 1.25.
Step 3: Calculate the difference in the function values.
In this case, the difference is f(2) - f(1) = 1.25 - 5 = -3.75.
Step 4: Calculate the difference in the x-values.
The difference in this case is 2 - 1 = 1.
Step 5: Calculate the average rate of change.
Divide the difference in the function values by the difference in the x-values to get:
Average rate of change = (-3.75) / 1 = -3.75.
Therefore, the average rate of change of the function f(x) = 20(1/4)^x from x = 1 to x = 2 is -3.75 (as a decimal).