Question

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.

Answer 1

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

Answer 2

after another 2 generation

Answer 3

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?

Answer 4

take note with the carrying capacity

Answer 5

dn1/dt=r1n1

Answer 6

\[dn2/dt =r2n2\]

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

yes

Answer 11

ok

Answer 12

is this for a differential equations class

Answer 13

get the mean of the r

Answer 14

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

Answer 15

either

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

ok

Answer 20

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

Answer 21

do you know the answer?

Answer 22

we only have one strain
n

Answer 23

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

Answer 24

thank you very much, take care and GOD BLESS

Answer 25

your a great help, thanks a lot

Answer 26

bye