anonymous
  • anonymous
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.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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alekos
  • alekos
So you need to find V'(t) then substitute t = 100
anonymous
  • anonymous
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
  • anonymous
V' (100)= 3* (-.0024) *(1-e^ -.24)^2 ??

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alekos
  • alekos
That's close but not quite right. I'm just checking to see if my method agrees with your answer
alekos
  • alekos
Your answer is in cubic centimeters but the question asks for the rate of change?
anonymous
  • anonymous
The answer is 0.103 cm^3/ month
alekos
  • alekos
OK, still checking
alekos
  • alekos
Yes, that answer is correct! Now for my solution.
anonymous
  • anonymous
. . . and your solution is ? . . .
alekos
  • alekos
the equation editor isn't working
alekos
  • alekos
V'(t) =(72/25)e^(-9t/1250)(e^(3t/1250) -1)^2
alekos
  • alekos
Substituting t=100 => V'(100) = 0.103
anonymous
  • anonymous
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
  • alekos
V'(t) is the rate of change of V(t) which is the derivative
anonymous
  • anonymous
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
  • alekos
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
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alekos
  • alekos
So you can take that all back
alekos
  • alekos
If you substitute t=100 (or x=100) into that equation you'll get 0.1032 cc/mth
alekos
  • alekos
Cat got your tongue?
alekos
  • alekos
Ah, you got nothing to say now. So I'm not full of hot air like you might have thought. Your welcome

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