Recent content by cango91

I tried to generalize it. It can be any period. Also this expression can be used for population growth where a certain amaunt of individuals die periodically (i.e. anti-viral in virus growth) or where there is periodical immigration.

Thank you very much for your help. If I'm not mistaken the expression becomes: P_{f}=P_{0} e^{kt}+ \frac{a(1-e^{kt})}{1-e^{k}} where P_{f} denotes future value of the money, P_{0} denotes the initial amount of the money, r denotes the annual percent interest and t denotes the total number...

You're right about the summation. I must have added the +k at the end by mistake. So is this a mathematically correct approach? Thank you very much by the way...

Hmm I think I figured something out: The total amount of money at month m is: Pfinal=P0emr+((from t=0 to m-1)\Sigma)ket)+k Can you please check if this statement is true

Initially: P 1st Month: Pe^r + k 2nd month: (Pe^r + k)e^r + k 3rd month: ((Pe^r + k)e^r + k)e^r +k 4th month: (((Pe^r + k)e^r + k)e^r +k)e^r + k . . . So?

from P*e^(rt) P for the second month is 2.6, r=0.5 t=1

Is there any equation/formula for continuous compound interest to which money is added (or substracted from) periodically? Or can one be derived? Thanks i.e. monthly interest rate is 50% and we add 1$ every month (:bugeye:) Initially: 1$ 1st Month: 1.6 + 1 = 2.6$ 2nd month: 4.3 + 1...

[RESOLVED]General question about growth function? P=P0ekt I'm given that a population doubles in number in 4 hours. Does that mean the k in the function equals 0.5 per hour or should I find k from 2=e4*k ?

I tried to find the equation without solving the D.E... Is my solution still wrong then?

But regardless of the growth rate 50000 will die per hour. P0ekt is the number of individuals if there were no deaths but there are 50 000 deaths per hour so I added the expression -50000*t .. Why should I divide by k?

Hmm... You're right... So would this be a correct equation for the problem I stated? Pnew = P0ekt - 50000*t

I am trying to model the growth of a population which replicates at a rate of 160% every four hours. Also 50 000 members die every hour. so t denoting time in hours, P denoting the population, k being 0.4 I wrote: dP/dt=kp-50 000 *t Is my approach to solving the differential faulty...

This is potentially one of the 10 questions to be asked in tomorrow's 45 minutes exam, there should be a quicker way... Plus expanding the whole expression would be too long and impractical.. Thanks anyways, any other suggestions?

Homework Statement \int sin^{11}x.dx Homework Equations The Attempt at a Solution \int (sin^{2}x)^{5}.sinx.dx \int (1-cos^{2}x)^{5}.sinx.dx let cosx be u, statement became - \int (1-u^{2})^{5}.du and I'm stuck here. Any help is appreciated, thank you