3 Equilibration: y,=r(y-yo) dN 1. The limiting capacity of the habitat of a wild
ID: 2890103 • Letter: 3
Question
3 Equilibration: y,=r(y-yo) dN 1. The limiting capacity of the habitat of a wildlife herd is 750. The growt rate of the herd's population N is proportional to the unutilized opportunity for growth, as described by the dN year size of the population is 160. What is the size of the population at all times after the start of the project! 2. Isaac Newton's law of cooling is a model of the rate T' at which the temperature T' of an object changes in time t when the object is in an environment that is at temperature To. The law states T' -(To -T) where r characterizes how quickly heat can be transferred between the environment and the object A satellite is orbiting the earth and is warmed by the sun. Just before the satellite enters the shadow of the sun its temperature is 400 Kelvin. The temperature of space is 3 Kelvin. Because outer space is nearly a vacuum, the rate at which heat can be transferred from an an object in space to the diffuse gas that occupies outer space is very low: r-10- What function describes the temperature of the satellite as a function of time t in hours since the satellite has entered the shadow of the earth according to Newton's law of cooling? (Note: You need to introduce nicknames for the quantity to be described and the independent variable including units.)Explanation / Answer
This is the solution to problem 1. We experts are allowed only to solve only 1 problem.
dN/dT = 0.1(750-N)
At T=0, N = 160
dN/(750-N) = 0.1dT
Integrating both sides,
left limit = 0 to N
right limit = 0 to T
-ln(750-N) + c = 0.1T
At T=0, N = 160
substituting these values to get the value of c
c = ln(750-160)
c = ln(590)
Therefore,
ln(590/750-N) = 0.1T
(590/(750-N)) = e^0.1T
(590e^(-0.1T))=750-N
N = 750 - (590e^(-0.1T))
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