by joelbear 14 Replies latest jw friends
Okay, a related rates problem that has me stumped.
You have rabbits and wolves in a forrest. Their relationship is
given as RABBITS = 1500 / (1 + WOLVES)
The number of Wolves increasing at a rate of 1/8 per year. What is the increase or decrease in the number of rabbits in the year that there are 80 Wolves.
Thanks
Joel
Slightly more than the publishers in Afghanistan.
Joel,
This looks like arithmetic to me, rather than calculus. For this year, the number of rabbits is 1500 divided by 81 which is 18.52. We will forget that we can not have fractions of rabbits. Last year there were 71.11 wolves and 20.80 rabbits, or a difference of 2.28 rabbits. Therefore, there was a decline in rabbits of 10.96%
Teacher! Teacher! Did I get it right, did I, did I?
joelbear,
Let W=yearly number of Wolves, R=yearly number of Rabbits, then
R = 1500/(1+W).
Differentiate with respect to time, we get:
dR/dt = -1500/((1+W)^2) * dW/dt.
dW/dt = 1/8, and when W=80, we get:
dR/dt = -1500/(81*81*8) = -0.02857 = -1/34.992.
So when the number of wolves is 80, the rabbit population is
DECREASING at the rate of approximately -1/35 rabbits per year.
Hope this helps.
VM44
I don't think VM44's solution will help much, because the answer he obtains is wrong. The actual answer, based on calculus, is -2.29 rabbits. VM44 went wrong by using dW/dt = 1/8 instead of (1/8)*80. If he had included the factor of 80, he would have obtained a number 80 times as large as the one he reported: (-1/34.992)*80 = -2.29.
Joseph F. Alward
"Skeptical Views of Christianity and the Bible"
Taking into account all the cars that travel our highways, and all the tyres that consequently need to be changed through wear.
Where does all the rubber go that as worn off them?
Radar
Like all people who have nothing, I lived on dreams
Addendum to the rabbit-wolf problem:
If the growth of the wolf population is assumed to be exponential, then the actual decline in the number of rabbits is 2.20. (This is obtained by integrating the dR/dt, assuming that the wolf population is 80 at the beginning of the year.)
Joseph F. Alward
"Skeptical Views of Christianity and the Bible"
JosephAlward
You have not taken into account environmental issues, other predators, disease etc.
and another thing: how does a thought begin and materialise?
Radar
Like all people who have nothing, I lived on dreams
JosephAlward is correct, a factor of 80 is missing in my answer.
I made a mistake in interpreting the value for the yearly rate of Wolf
increase.
A yearly increase in wolves of 1/8 does not make sense!
The value of 1/8 is the FRACTIONAL yearly rate of increase
for the wolves, or
(dW/dt)/W = 1/8,
this does makes sense!
The experession for dR/dt in my previous post is still correct, but
is modified by multiplying and dividing by W on the right hand side:
dR/dt = -(1500/((1+W)^2))*W *((dW/dt)/W)
= -((1500*80)/(81*81)) * (1/8) = -2.286.
this value is consistent with JosephAlward and larc's numbers.
--VM44
VM44
I can tell you certainly aren't part of the faithful & discreet slave class.They never mess up, and if they do, they never admit it and explain why.
