The cost (in dollars) of producing x units of a certain commodity is c(x)=5000+10x+0.05x^2
Find A=100 to x=105
so far i got
y-y/x-x= C(105)-C(100)/105-105
i don't understand how it comes out to be 101.25/5
please help me
You have not said what A is. You also introduce y without definition. You need to add parentheses to clarify your y-y/x-x equation.
Please restate the problem exactly as it was presented to you.
I appears that you are attempting to calculate the average rate of change of the cost as the number of units changes from 100 to 105
that rate would be [C(105)-C(100)]/[105-100]
which does work out to be 101.25/5
wait so whats is c(105) is it 5000+10x+0.05x^2 times 105?
It appears you are not familiar with the function notation.
In short
if C(x) = 5000+10x+0.05x^2
then C(105) = 5000 + 10(105) + .05(105)^2
(whenever an x appeared, we replaced it with 105, the same thing with C(100) )
To find the average rate of change of a function, we use the formula:
average rate of change = (f(b) - f(a))/(b - a)
In this case, we are given the function c(x) = 5000 + 10x + 0.05x^2 and we want to find the average rate of change from A = 100 to x = 105.
Substituting the values in the formula, we have:
average rate of change = (c(105) - c(100))/(105 - 100)
To find c(105), we substitute x = 105 into the function:
c(105) = 5000 + 10(105) + 0.05(105)^2
c(105) = 5000 + 1050 + 551.25
c(105) = 6601.25
Next, to find c(100), we substitute x = 100 into the function:
c(100) = 5000 + 10(100) + 0.05(100)^2
c(100) = 5000 + 1000 + 500
c(100) = 6500
Now plugging these values back into the formula for average rate of change:
average rate of change = (6601.25 - 6500) / (105 - 100)
average rate of change = 101.25 / 5
The result simplifies to 20.25.
Therefore, the average rate of change, from A = 100 to x = 105, is 20.25 dollars.