Ask your own question, for FREE!
Mathematics 58 Online
OpenStudy (anonymous):

can some on please help me on a "wombat island" question, its a pretty long question, i will show you bit by bit. please help

OpenStudy (anonymous):

A model for number of wombats “W” on a island, ‘t’ years after the initial 200 are settled there , takes into account the availability of wombat food. The model is dW/dt= (m-n-kW)W Where m is the birth rate and n is the death rate of the wombats. k is a constant related to the amount of food. Suppose the m=0.1 and the n=0.06 and k=0.00005 a) Find an expression for the number of wombats after ‘t’ years? b) According to the model, find the wombat population after (i) 10 years (ii) 100 years c) At what time is the wombat population increasing most rapidly? d) Explain the effects of term ‘-kW’ on the growth rate of the wombat population?

OpenStudy (anonymous):

come on its my first question , please help someone? >.<

OpenStudy (unklerhaukus):

Hello viktorhh, Welcome to Open Study, Wombats are a function of time W(t) ! \[\frac{\text dW}{\text dt}= (m-n-kW)W \] \[m=0.1\qquad n=0.06\qquad k=0.00005\]

OpenStudy (anonymous):

ye thats right man!

OpenStudy (anonymous):

thanks

OpenStudy (unklerhaukus):

i think it is probably a good idea to lump the constants \(m\) and \(n\) together \[m-n=0.1-0.06=0.04=c\]

OpenStudy (unklerhaukus):

\[\frac{\text dW}{\text dt}= (c-kW)W\], now separate the variables \[\frac{\text dW} {(c-kW)W}={\text dt}\] and you can integrate \[\int\frac{\text dW} {(c-kW)W}=\int{\text dt}\]

OpenStudy (anonymous):

so, i ll just sub into all the numbers now and get question(a) . thanks

OpenStudy (unklerhaukus):

dont put the numbers in yet

OpenStudy (anonymous):

how come?

OpenStudy (unklerhaukus):

what would happen if you did ?

OpenStudy (anonymous):

dont i need to find an expressoin for of number of wombats after ‘t’ years?

OpenStudy (unklerhaukus):

yeah before you can determine the number of wombats, you need to turn the differential equation into a equation without derivatives in in W(t) rather than W'(t)

OpenStudy (unklerhaukus):

in it*

OpenStudy (anonymous):

ok

OpenStudy (unklerhaukus):

you might use partial fractions on the integrand before integrating

OpenStudy (anonymous):

i used cas, it come out to be|dw:1342447906126:dw|

Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!
Latest Questions
MAGABACK: ART!
9 minutes ago 5 Replies 0 Medals
danielfootball123: Is Donald trump a good president?
2 hours ago 92 Replies 6 Medals
Gucchi: chem help
13 hours ago 9 Replies 0 Medals
Can't find your answer? Make a FREE account and ask your own questions, OR help others and earn volunteer hours!

Join our real-time social learning platform and learn together with your friends!