[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?

[TenOfThem]

(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

[PeteyB26]

You can differentiate P to give Ake^kt
Then you can use that with t=0 to find values for A and K

[sexbo]

You can't differentiate e^x? Lawl.

[steve2005]

(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

[raheem94]

(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.

[raheem94]

(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'.

[steve2005]

(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 ..)

[Gilsenan]

Thanks guys, got it now The question is correct, I've double checked.

[raheem94]

(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,

[steve2005]

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

Is this the solution?




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[raheem94]

(Original post by steve2005)
Is this the solution?




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