Calculus
The following formula accurately models the relationship between the size of a certain type of a tumor and the amount of time that it has been growing:
V(t)=400(1-e^ -.0024t)^3

where t is in months and V(t) is measured in cubic centimeters. Calculate the rate of change of tumor volume at 100 months.

Question

Calculus
The following formula accurately models the relationship between the size of a certain type of a tumor and the amount of time that it has been growing:
V(t)=400(1-e^ -.0024t)^3
 
where t is in months and V(t) is measured in cubic centimeters. Calculate the rate of change of tumor volume at 100 months.

alekos · Answer

So you need to find V'(t) then substitute t = 100

anonymous · Answer

correct. Substituting 100 for t results in an exponent of -.24

The answer is 0.103 cm^3
but I don't know how to arrive at that answer.

anonymous · Answer

V' (100)= 3* (-.0024) *(1-e^ -.24)^2 ??

alekos · Answer

That's close but not quite right.  I'm just checking to see if my method agrees with your answer

alekos · Answer

Your answer is in cubic centimeters but the question asks for the rate of change?

anonymous · Answer

The answer is 0.103 cm^3/ month

alekos · Answer

OK, still checking

alekos · Answer

Yes, that answer is correct!  Now for my solution.

anonymous · Answer

. . . and your solution is ? . . .

alekos · Answer

the equation editor isn't working

alekos · Answer

V'(t)  =(72/25)e^(-9t/1250)(e^(3t/1250) -1)^2

alekos · Answer

Substituting t=100 => V'(100) = 0.103

anonymous · Answer

What do the numbers V'(t)  =(72/25)e^(-9t/1250)(e^(3t/1250) -1)^2
have to do with the equation  V(t)=400(1-e^ -.0024t)^3

alekos · Answer

V'(t) is the rate of change of V(t)  which is the derivative

anonymous · Answer

That is an obvious statement, which does nothing towards helping to answer the question to which you and I have been engaged with over the last hour. 

You have provided no help in one hours time. If you do not know how to solve the question, why would you pretend and waist anyone's time?

alekos · Answer

No you're mistaken, I'm not wasting your time.
Here is the solution to the derivative step by step but I used the variable x instead of t.   Had to use my  word equation editor

alekos · Answer

So you can take that all back

alekos · Answer

If you substitute t=100 (or x=100) into that equation you'll get 
0.1032 cc/mth

alekos · Answer

Cat got your tongue?

alekos · Answer

Ah, you got nothing to say now.  So I'm not full of hot air like you might have thought.  Your welcome