Suppose
f(t)=sqrt(3t+3)
What is the average rate of change of f(t) with respect to t as t changes from 2 to 2.01?
The AROC is:_____
f(2.01) = √9.03
f(2) = √9
avg rate of change = (√9.03 - √9)/(2.01-2)
= ....
I get .49958..
Yes that is correct. This is what i got also after working it 10 times haha.
why did you doubt it ?
To find the average rate of change of a function, we need to calculate the difference in the function values at the endpoints of the interval divided by the difference in the corresponding input values.
In this case, we want to find the average rate of change of the function f(t) = √(3t + 3) as t changes from 2 to 2.01.
Step 1: Calculate the function values at the endpoints.
Plug in t = 2 into the function:
f(2) = √(3 * 2 + 3) = √(6 + 3) = √9 = 3
Now, plug in t = 2.01 into the function:
f(2.01) = √(3 * 2.01 + 3) = √(6.03 + 3) = √9.03 ≈ 3.005
Step 2: Calculate the difference in the function values.
Difference in function values = f(2.01) - f(2) ≈ 3.005 - 3 ≈ 0.005
Step 3: Calculate the difference in the corresponding input values.
Difference in input values = 2.01 - 2 = 0.01
Step 4: Calculate the average rate of change.
Average rate of change = Difference in function values / Difference in input values
AROC ≈ 0.005 / 0.01 = 0.5
Therefore, the average rate of change of f(t) with respect to t as it changes from 2 to 2.01 is approximately 0.5.