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4 MA 36600 LECTURE NOTES: MONDAY, FEBRUARY 9 so that we have the equation 0=(1 . 01) 48 · 10000+ 1 (1 . 01) 48 1 (1 . 01) b = 0 = 16122 . 261+61 . 223 b = b = 16122 . 261 61 . 223 = 263 . 338 . Hence we must pay at least $263.34 each month in order to pay of the loan in 4 years. Nonlinear Equations. Recall the logistic diferential equation dy dt = ry ° 1 y K ± For some (positive) constants r and K . The associated diference equation is in the Form y n t n = ry n ° 1 y n K ± where t n = h. We can place this diference equation in the Form y n +1 = y n + ry n ° 1 y n K ± h =(1+ hr ) y n ² 1 hr (1 + hr ) K y n ³ . Make the substitution u n = hr (1 + hr ) K y n = u n +1 = ρu n (1 u n ) in terms oF the constant ρ =1+ hr . We call this equation the logistic diference equation . Note that this equation is not a linear equation. We ask two questions: #1: What are the equilibrium solutions u L ? #2: Can we ±nd a Formula For the exact solution u n , such as For linear equations?
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This note was uploaded on 11/30/2011 for the course MATH 366 taught by Professor Edraygoins during the Spring '09 term at Purdue.

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