Stitz-Zeager_College_Algebra_e-book

# The logistic growth model combines the law of

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Unformatted text preview: nswer anyway, why not use it earlier to simplify the computations? It is a fair question which we answer unfairly: it’s our book. 6.3 Exponential Equations and Inequalities y= x= 5ex ex + 1 5ey ey + 1 365 Switch x and y x (ey + 1) = 5ey xey + x = 5ey x = 5ey − xey x = ey (5 − x) x ey = 5−x ln (ey ) = ln y = ln We claim f −1 (x) = ln x 5−x x 5−x x 5−x . To verify this analytically, we would need to verify the compositions f −1 ◦ f (x) = x for all x in the domain of f and that f ◦ f −1 (x) = x for all x in the domain x of f −1 . We leave this to the reader. To verify our solution graphically, we graph y = f (x) = e5e x +1 x and y = g (x) = ln 5−x on the same set of axes and observe the symmetry about the line y = x. Note the domain of f is the range of g and vice-versa. y = f (x) = 5ex ex +1 and y = g (x) = ln x 5 −x 366 Exponential and Logarithmic Functions 6.3.1 Exercises 1. Solve the following equations analytically. (a) 3(x−1) = 27 (b) 3(x−1) = 29 (c) 3(x−1) = 2x (h) (l) 2(x 7e2x = (m) (d) = x= 1 (e) 8 128 (f) 37x = 814−2x 0.06 12t 12 −5730k = 1 e 2 (j) 1 + (k) 3 − x) e2x =1 =...
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