Stitz-Zeager_College_Algebra_e-book

1602t 165 1 whose solution is t 01602 ln 37 322 it

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Unformatted text preview: nterval (10 ln(3), ∞). Our sign diagram is below, and next to it is our graph of t = T (t) from Example 6.1.2 with the horizontal line y = 100. y 180 160 140 (+) 0 0 (−) 10 ln(3) 120 y = 100 80 60 H.A. y = 70 40 20 2 4 6 8 10 12 14 16 18 20 t y = T (t) In order to interpret what this means in the context of the real world, we need a reasonable approximation of the number 10 ln(3) ≈ 10.986. This means it takes approximately 11 minutes for the coffee to cool to 100◦ F. Until then, the coffee is warmer than that.8 We close this section by finding the inverse of a function which is a composition of a rational function with an exponential function. 5ex is one-to-one. Find a formula for f −1 (x) and check ex + 1 your answer graphically using your calculator. Solution. We start by writing y = f (x), and interchange the roles of x and y . To solve for y , we first clear denominators and then isolate the exponential function. Example 6.3.4. The function f (x) = 8 Critics may point out that since we needed to use the calculator to interpret our a...
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