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Mathematics 42 Online
OpenStudy (anonymous):

Let the reproductive rates in four successive generations of a population be 4,2,3,2. If the population has a size of 10 million individuals at the end of this four-generation period, how large will it be after another two generations if there is no regulation of growth? Carrying capacity is 100 million.

OpenStudy (dumbcow):

do you expect the pattern to continue? 4,2,3,2,2,2...

OpenStudy (anonymous):

after another 2 generation

OpenStudy (dumbcow):

ok so then after the next generation with a reproductive rate of 2 it would grow 200% to 30 million ->10(1+2) = 30 Repeating this for the next generation 30(1+2) = 90 90 million is that right?

OpenStudy (anonymous):

take note with the carrying capacity

OpenStudy (anonymous):

dn1/dt=r1n1

OpenStudy (anonymous):

\[dn2/dt =r2n2\]

OpenStudy (anonymous):

the rate of increase of the total population is \[dN/dt =r1n1+r2n2 = mean of the r's(N)\]

OpenStudy (dumbcow):

does n1 refer to initial population, n2 second generation and r1 is reproductive rate

OpenStudy (anonymous):

Let N be the total population number; N = n1 + n2.

OpenStudy (anonymous):

yes

OpenStudy (dumbcow):

ok

OpenStudy (dumbcow):

is this for a differential equations class

OpenStudy (anonymous):

get the mean of the r

OpenStudy (dumbcow):

the mean of the rates is 15/6 for all generations, how does that help? im sorry im not following or helping you :(

OpenStudy (anonymous):

either

OpenStudy (anonymous):

dn2/dt=n2(r2-mean of r (N)/K K is the carrying capacity

OpenStudy (dumbcow):

so dn2/dt = n2(2 - 15/6) / 100 mill ->dn2/dt = -n2/200 what is n2?

OpenStudy (dumbcow):

if we integrate both sides and solve for n2 -> n2 = e^-t/200

OpenStudy (anonymous):

ok

OpenStudy (dumbcow):

but the problem only refers to generations not time, so to get a number for n we need a t ??

OpenStudy (dumbcow):

do you know the answer?

OpenStudy (anonymous):

we only have one strain n

OpenStudy (dumbcow):

ok well i gotta go, good luck hope you find someone to help you sorry

OpenStudy (anonymous):

thank you very much, take care and GOD BLESS

OpenStudy (anonymous):

your a great help, thanks a lot

OpenStudy (anonymous):

bye

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