Assignment 20

course Mth 174

???????W??????assignment #020020. `query 20

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Cal 2

11-23-2007

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12:32:07

Query problem 11.7.6 plot (dP/dt) / P vs. t, where P is a solution to 1000 / P dP/dt = 100 - P with initial population P = 0.{}{}Can P(t) ever exceed 200?{}{}Can P(t) ever drop below 100?

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The population will exceed over 200 if the initial population is 200 as seen in the problem. The population may drop below 100 it all depends on if the individuals get sick or start having a serious disease go around within the population. But it will exceed 200 individuals though.

The solution is to be done in terms of the given function and initial conditions.
1000 / P * dP/dt = 100 - P is rearranged to
dP / ( P ( 100 - P) ) = dt / 1000, then is solved by integrating both sides of the equation.
What do you get when you integrate both sides?
What is the resulting solution for the given initial conditions?

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12:32:35

Query problem THIS PROBLEM DOES NOT EXIST IN THE NEW EDITION 11.7.10 plot (dP/dt) / P vs. t for given population data and estimate a and b for 1 / P dP/dt = a - bt; solve and sketch soln. sample pop: 1800 5.3, 1850 23.1, 1900 76, 1950 150, 1990 248.7

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sorry can not follow this problem.

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12:32:37

what are your values of a and b?

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12:32:41

What are the coordinates of your graph points corresponding to years 1800, 1850, 1900, 1950 and 1990?

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12:32:43

According to your model when will the U.S. population be a maximum, if ever?

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12:32:44

Give your solution to the differential equation and describe your sketch of the solution.

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12:34:57

describe your graph of dP/dt vs. P, P>0

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the describtion of the graph goes as follows. It continues to go up gradually having a even slope the whole way never really dropping off or anything just almost like a straight line.

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12:37:45

describe the approximate shape of the solution curve for the differential equation, and describe how you used your previous graph to determine the shape; describe in particular how you determined where P was increasing and where decreasing, and where it was concave of where concave down

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The approximate shape of the solution curve for the differential equation is just like a right side up V. it crosses the x-axis at (0,0) going down to make the curve to go back up and crossing the x-axis again at (6,0). so the only thing that is going on here is that it is concave up. At first the population is decreaseing and once it gets to the bottom it is increasing again.

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12:39:01

describe how the nature of the solution changes around P = 6 and explain the meaning of the term 'threshold population'.

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the nature of the solution changes around P = 6 because it starts to go back increasing again for just a brief period of time. The meaning of the term threshold population describes when a population gets to its greatest capacity before it starts to be over crowded.

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12:46:12

what are your estimates of the maximum and minimum robin populations, and what are the corresponding worm populations?

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the max and min values of the robin populations which are only estimates are 1 and 3. the worm populatoins corresponding to these estimates of robin populations would be 3 and 1 because there would be more worms with only 1 robin and be less worms 1 when there are 3 robins.

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12:46:57

Explain, if you have not our a done so, how used to given slope field to obtain your estimates.

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already done so

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12:47:23

Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

didnt really understand that one problem that was not in my book so i didnt do it because i couldnt follow it.

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Please respond to the questions posed in my notes.

end of document

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