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Mth 174
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Question Form_labelMessages **
Assignment 17 Question
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Question:
Query problem 11.2.8 (4th edition 11.2.5 3d edition 11.2.4) The slope field is shown. Plot solutions through (0, 0) and (1, 4).
Describe your graphs. Include in your description any asymptotes or inflection points, and also intervals where the graph is concave up or concave down.
Your solution:
Confidence Assessment:
Given Solution:
RESPONSE -->
Solution through (0,0): concave up from (0,0) to about (3,3) then concave down for t>3, point of inflection at (3,3), horizontal asymptote at P=10. Graph appears to be P=0 for all t<0. Since givens include P>=0, no graph for negative P.
Solution through (1,4): concave up from (-1,0) to about (2,3) , then concave down for t>2, point of inflection at (2,3), horizontal asymptote at P=10. Graph appears to be P=0 for at t<-1. Since givens include P>=0, no graph for negative P.
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14:13:09
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I'm confused how you came to that solution. The problem in the book says: The slope field for the equation dP/t = 0.1P(10-P) for P>= 0. Plot the solutions through the following points: (0,0), (1,4), (4,1) ,(-5, 1), (-2, 12), and (-2, 10). Is this the correct problem? If so I'm confused about you set the problem up and how you ended up with the points in your solution.
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It would have been good for you to also include your own thinking on the problem. However you are correct that the given solution doesn't match the graph very well.
Here's a much better description:
The slope of the graph on the horizontal axis is zero at every point. So the solutoin through (0, 0) simply stays on that axis. The solution function would be P(t) = 0.
Starting at (1, 4) and moving to the right the solution curve rises very quickly at first, then less and less quickly, becoming asymptotic to the line P = 10. The slope becomes 1 somewhere around (3, 9) and continues decreasing beyond that point. Moving to the left from (1, 4) the solution curve descends very quickly at first, then less and less quickly, crossing the y axis around (0, 3/2) and becoming asymptotic to the negative horizontal axis.
What are your description for the other given starting points?
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