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# C3 help - differentiating lnx and e^x

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1. 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?
2. (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
3. You can differentiate P to give Ake^kt
Then you can use that with t=0 to find values for A and K
4. You can't differentiate e^x? Lawl.
5. (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
6. (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.
7. (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?

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

Now differentiate, , with respect to 't' and then sub in t=0 and dP/dt=6 to find the value of 'k'.
8. (Original post by raheem94)

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

Now differentiate, , 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 ..)
9. Thanks guys, got it now The question is correct, I've double checked.
10. (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:
Show

When we sub in t=0 and P=3, we can find A, A=3.

When t=0, dP/dt=6,

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

Is this the solution?

12. (Original post by steve2005)
Is this the solution?

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

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