Question

Help me with question 7i) http://www.xtremepapers.com/papers/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_w07_qp_3.pdf

Answer 1

dN /kN = cos (0.002)dt
(kN)^-1 dN = cos (0.02t) dt
ln (kN) = sin 0.02t/0.02 + c
is this right so far?

Answer 2

Congratulations! xtremepaper is down for me.

Answer 3

you cant open?

Answer 4

I can't. Can you upload the file?

Answer 5

erm could you check the my differentiation first?

Answer 6

What is N?

Answer 7

I can't even see the question.

Answer 8

The number of insects in a population t days after the start of observations is denoted by N. The variation in the number of insects is modelled by a differential equation of the form
dN/dt= kN cos(0.02t), where k is a constant and N is taken to be a continuous variable. It is given that N = 125 when t = 0.
(i) Solve the differential equation, obtaining a relation between N, k and t.

Answer 9

That looks right to me.

Answer 10

Wait. I think it is actually k ln(t) on the left hand side.

Answer 11

No I mean \(\dfrac{1}{k}\ln(N)\)

Answer 12

I have to go. Read later.

Answer 13

Okay thankss.

Answer 14

the differentiation is right but i think k usually belongs more naturally on RHS of equation. ie

ln (N) = ksin 0.02t/0.02 + c

Answer 15

ohh okay. the final equation is ln N = 50ksin(0.02t) + ln 125. Where does 50 come from?

Answer 16

50 is 1/0.02!!!!!

Answer 17

OHHHHH. Okay. hahah thanks.