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C3 help - differentiating lnx and e^x

The question is:

9) In a biological compound, bacteria are being grown in a culture. The mass of the bacteria at time t hours is P milligrams. At time t = 0, p = 3 and dP/dt = 6.

(i) A standard model for this situation is given by P = Ae^kt, where A and K are constants.

a) Write down dp/dt in terms of A, k and t. Find the values of A and k.

I don't understand what it wants me to do really, because it isn't simply differentiating P is it?
Reply 1
Avatar for TenOfThem
TenOfThem
18
Original post by Gilsenan


I don't understand what it wants me to do really, because it isn't simply differentiating P is it?



Yes it is

You have both P and P' at t=0 so can find all of the constants
Reply 2
Avatar for PeteyB26
PeteyB26
You can differentiate P to give Ake^kt
Then you can use that with t=0 to find values for A and K
Reply 3
Avatar for sexbo
sexbo
You can't differentiate e^x? Lawl.
Reply 4
Avatar for steve2005
steve2005
17
Original post by Gilsenan
The question is:

9) In a biological compound, bacteria are being grown in a culture. The mass of the bacteria at time t hours is P milligrams. At time t = 0, p = 3 and dP/dt = 6.

(i) A standard model for this situation is given by P = Ae^kt, where A and K are constants.

a) Write down dp/dt in terms of A, k and t. Find the values of A and k.

I don't understand what it wants me to do really, because it isn't simply differentiating P is it?


I don't think you have copied the question correctly.

Do you mean at t=0, p = 3

or do you mean that when p = 3 , dp/dt = 6
Reply 5
Avatar for raheem94
raheem94
13
Original post by steve2005
I don't think you have copied the question correctly.

Do you mean at t=0, p = 3

or do you mean that when p = 3 , dp/dt = 6


The question is correct.

At t=0, p=3 and dp/dt=6.
Reply 6
Avatar for raheem94
raheem94
13
Original post by Gilsenan
The question is:

9) In a biological compound, bacteria are being grown in a culture. The mass of the bacteria at time t hours is P milligrams. At time t = 0, p = 3 and dP/dt = 6.

(i) A standard model for this situation is given by P = Ae^kt, where A and K are constants.

a) Write down dp/dt in terms of A, k and t. Find the values of A and k.

I don't understand what it wants me to do really, because it isn't simply differentiating P is it?


P=Aekt \displaystyle P=Ae^{kt}

Sub in P=3 and t=0, in the above equation to find the value of A.

Now differentiate, P=Aekt \displaystyle P=Ae^{kt} , with respect to 't' and then sub in t=0 and dP/dt=6 to find the value of 'k'.
Reply 7
Avatar for steve2005
steve2005
17
Original post by raheem94
P=Aekt \displaystyle P=Ae^{kt}

Sub in P=3 and t=0, in the above equation to find the value of A.

Now differentiate, P=Aekt \displaystyle P=Ae^{kt} , with respect to 't' and then sub in t=0 and dP/dt=6 to find the value of 'k'.


Why are you so sure the question is correct. The problem is that when t = 0 the k is impossible to evaluate. ( At least that's what I think ..)
Reply 8
Avatar for Gilsenan
Gilsenan
OP
1
Thanks guys, got it now :smile: The question is correct, I've double checked.
Reply 9
Avatar for raheem94
raheem94
13
Original post by steve2005
Why are you so sure the question is correct. The problem is that when t = 0 the k is impossible to evaluate. ( At least that's what I think ..)


'k' can be evaluated when you find dP/dt.

See the spoiler

Spoiler

Original post by Gilsenan
Thanks guys, got it now :smile: The question is correct, I've double checked.



Is this the solution?




Uploaded with ImageShack.us
Reply 11
Avatar for raheem94
raheem94
13
Original post by steve2005
Is this the solution?




Uploaded with ImageShack.us


Yes, its correct. I have a similar solution in the spoiler in my post.

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