MAT2705-01/02 16F Test 1 Print Name (Last, First) _________________________________|__Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use EQUAL SIGNS and arrows when appropriate. Always SIMPLIFY expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC). [Recall you need 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 instead of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiJ0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdRJjAuMGVtRictRjk2LlEiLEYnRjJGPEY+L0ZBRjFGQkZERkZGSEZKL0ZNRlEvRlBRLDAuMzMzMzMzM2VtRidGK0YyRjw= in your differential equation for an unknown variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn for Maple to interpret the prime as a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn derivative.]
1. 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
a) Locate the points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JVEiMUYnRjRGN0Y0RjdGNEY3RjRGNw== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYlUSIyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYuUSIsRidGNEY3LyUmZmVuY2VHRjYvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGNi8lKnN5bW1ldHJpY0dGNi8lKGxhcmdlb3BHRjYvJS5tb3ZhYmxlbGltaXRzR0Y2LyUnYWNjZW50R0Y2LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY0RjdGNEY3RjRGNw== on the direction field plot and carefully draw in the solution curves through those points.b) Put the DE into standard form for a linear first order DE.c) Find the general solution.d) Find the solutions of the two initial value problems with the initial points LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMUYnRjQvJStleGVjdXRhYmxlR0Y9RjRGNEZURjQ= (=sol1) and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMC8lK2V4ZWN1dGFibGVHRj1GNEY0RlFGNA== (=sol2).e) Evaluate each of these solutions at 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. Evaluate your general solution there. What can you say about the solution curves for all initial data points with 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 ?f) Check your solution to the initial value problem with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiUtSSNtbkdGJDYlUSIyRidGMi9GNlEnbm9ybWFsRidGMkZBRjJGQS1JI21vR0YkNi5RIj1GJ0YyRkEvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZXRj1GMkZB following bob's method of checking any equation: replace the unknown everywhere in the equation and simplify both sides 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2. 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Birth and death rates of animal populations typically oscillate periodically with the passage of seasons, describable by the above simple model. Note that the growth rate function 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 varies periodically about its average value 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, indeed with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 one has purely exponential behavior 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.
a) Solve this initial value problem by the separable DE method. b) Suppose 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. Use the DE at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 to find the value of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn. What is the maximum percent that the population exceeds the average exponential growth during any given period (i.e., examine 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).c) What is the period of the oscillation? How many periods fit into one decay time of the exponential factor?solution1. linearLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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This deq will have problems at 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 where the slope field goes vertical, except at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIjBGJ0YyRjxGMkY8 , where the slope appears to be 1/4. In fact by eye one sees the straight line isocline solution passing through this point, but so do all other solutions for initial data to the right of this vertical asymptote in the direction field. The same must be true of data to the left. In other words, every solution passes through the point 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we interchange independent and dependent variables we get a constant function solution that represents the vertical asymptote.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. separable. population growthLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==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 maximum value of the ratio 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 is 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 the maximum percent increase is 0.96 %.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33 1/3 periods fit into one decay time. Hmm, like the records from the old days...Here are two plots for fun.LUklcGxvdEc2IjYkNyQqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCRJInRHRiQkIiIkISIjIiIiLUYpNiMsJC1JIipHRis2JCwkLUkkc2luR0YqNiMsJComSSNQaUdGK0YzRi9GMyIiIyQiIidGMiokRkAhIiIjRjNGQUYzRigvRi87IiIhJCIkTCRGRQ==LUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlNyYqJi1JJGV4cEdGJDYjLCRJInRHRickIiIkISIjIiIiLUYsNiMsJC1JIipHRiU2JCwkLUkkc2luR0YkNiMsJComSSNQaUdGJUYzRi9GMyIiIyQiIidGMiokRkAhIiIjRjNGQUYzRisqJkYrRjMtRiw2IywkLUY4NiRGQkZERkZGMyomRitGMy1GLDYjLCRGSyNGRUZBRjMvRi87IiIhRjMvSSZjb2xvckdGJzckSSRyZWRHRictSSIkR0YlNiRJJWdyYXlHRidGMQ==Look at the vertical tickmarks, you can see the 1 percent increase at the maximum compared to the exponential curve (red).3. saved for the 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JSFHpledge [Be sure to sign and date the pledge before handing in this test.]When you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet in on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: