[king0vdarkness]

Hi Everyone
just wondering if anyone could help me on this question:

The number of bacteria present in a culture at time t hours is modelled by the
continuous variable N and the relationship
N = 2000e^kt,
where k is a constant.
Given that when t = 3, N = 18 000, find
(b) how long it takes for the number of bacteria present to double, giving your
answer to the nearest minute
[The value of k is 1/3Ln9 (= 0.7324...)]

In the marksceme it starts off with 4000 = 2000e^0.7324t but I don't understand where the 4000 comes from.
Any help would be much appreciated. Thanks in advance!

[BabyMaths]

4000 = 2 x 2000.

They doubled 2000.

[king0vdarkness]

(Original post by BabyMaths)
4000 = 2 x 2000.

They doubled 2000.

cheers!

[king0vdarkness]

Sorry to bother you again but was wondering if you could help me with an integration question from c4 chapter 6 exercise 6e question 2e: integrate (cos2x)/(3+sin2x).

(I let y= Ln(e^2x+3) and differentiated and got 2(e^2x+3)/(e^2x+3) so i put I = 1/(2e^3)*Ln(e^2x+3) +c but the answer says I= 1/2Ln(e^2x+3) + c)

Thank You!

[BabyMaths]

(Original post by king0vdarkness)
integrate (cos2x)/(3+sin2x).
Thank You!

You can do this using the substitution u=3+sin 2x.

Alternatively try differentiating a few of these (with respect to x):





for some function of your choice.

If you see what's going on here then in future you can look out for integrals of the form

[BabyMaths]

(Original post by king0vdarkness)

I let y= Ln(e^2x+3) and differentiated and got 2(e^2x+3)/(e^2x+3) so i put I = 1/(2e^3)*Ln(e^2x+3) +c but the answer says I= 1/2Ln(e^2x+3) + c)

Thank You!

What are you trying to do here? Are you trying to find

Try the differentiation again.

[king0vdarkness]

(Original post by BabyMaths)
What are you trying to do here? Are you trying to find

Try the differentiation again.

yes how should i differentiate?

[king0vdarkness]

i let y = ln(e^2x+3), but when i differentiate i think im doing it wrong....

[king0vdarkness]

\int \frac{e^{2x}}{e^{2x}+3} dx sorry Ilyas! i meant this question!

[Venomilys]

(Original post by king0vdarkness)
\int \frac{e^{2x}}{e^{2x}+3} dx sorry Ilyas! i meant this question!

sigh...

[king0vdarkness]

sorry its displayed better in baby maths's last post