Rates involving two or more variables (1 Viewer)

[atakach99]

The number of burrows for a colony of rabbits is decreasing owing to the clearing of land, at a constant rate of 5 burrows per day. If the number of rabbits is given by the formula N= 5x^2 + 3X, where x is the number of burrows, find the rate of decrease in the rabbit population when there are 55 burrows.

I am having trouble answering this question. I know how to do it for when its increasing but i seem to get the question wrong when its decreasing.

plz help..

 

[tommykins]

回复: Rates involving two or more variables

dx/dt = -5

we're trying to find dn/dt when x = 55.

dn/dt = (dx/dt)*(dn/dx) by use of the chain rule.

derive N = 5x^2 + 3x, sub in x = 55 then you've got it.

Spoiler

dn/dx = 10x + 3

dn/dt = dn/dx * dx/dt = -5(10x+3) = -150x - 15

x = 55.

dn/dt = -150(55) - 15 -> answer.

 

[atakach99]

yea ok thnks man......just a little mistake -5 x 10 = -50

NOT = -150

thkns for the help