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# MAT109 Chapter 6 Study Guide MAT 109

Barry University

GPA 3.7

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This 8 page Study Guide was uploaded by Sterling Notetaker on Saturday September 10, 2016. The Study Guide belongs to MAT 109 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 9 views. For similar materials see Precalculus Mathematics 1 in Mathmatics at Barry University.

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Date Created: 09/10/16

MAT 109 Precalculus Mathematics 1 Chapter 6 Study Guide Notes L. Sterling September 16th, 2016 Abstract Provide a generalization to each of the key terms listed in this section. 1 Change-of-Base Formula log M = lob M a lob a 2 Composite Function (f ▯ g)(x) = f (g (x)) 3 Compound Interest Formula ▯ ▯ A = P a +r nt n 1 4 Continuous Compounding Formula rt A = Pe 5 e ▯ 1▯n lim 1 + = e n!1 n e ▯ 2:718 6 E▯ective Rate of Interest ▯ ▯ r n Compounding n times per yeae : r = n +▯ 1 r Continuous Compounding e r = e ▯ 1 7 Growth and Decay 7.1 Uninhibited Growth A = A0et 8 Horizontal Line Test 8.1 A function noting whether it’s one-to-one if the hori- zontal line hits the graph more than once or not. ▯1 9 Inverse Function f of f 9.1 f and f ▯1 ▯ f’s Domain=f1’s Range 2 ▯ f’ :Range=f▯1 ’s Domain x ! f (x) ! f▯1 (f (x)) = x ▯1 Domain of f : f (f (x)) = x ▯ ▯ x ! f ▯1(x) ! f f ▯1(x) = x ▯1 ▯ ▯1 ▯ Domain of f : f f (x) = x 10 Logistic Model 10.1 Function P (t) = c 1 + ae▯bt 10.2 Parts of the Function P : Population t : Time c : Constant [c > 0] e ▯ 2:718 a : Constant b : Constant 10.3 Growth and Decay Growth : b > 0 3 Decay : b < 0 11 Natural Logarithm y y = ln(x) ! x = e y = log (x) =10(x) ! x = 10y 12 Newtons Law of Cooling 12.1 Function u(t) = T + (0 ▯ T)e ; k < 0 12.2 Parts of the Function u : Temperature t : Time T : Constant Temperature u0: Initial Temperature e ▯ 2:718 k : Negative Constant k < 0 : Any Negative Constant Less Than 0 13 Present Value Formulas ▯ r▯▯nt P = A 1 + n 4 ▯rt P = Ae 14 Properties of Logarithms log 1 = 0 a logaa = 1 aloax = x logaa = y logabc = logab + logac y logax = y log a logab = logac [iff b = c] x x ln(a) a = e ▯ ▯ x loga = logax ▯ logay y ▯ ▯ x logax loa 6= y logay loa (xy) = logax + loa y loga(xy) 6= (loa x)(loa y) 5 15 Exponential Functions Properties 15.1 Function x f (x) = a a > 1 15.2 Domain All Real Numbers 15.3 Range All Positive Real Numbers 15.4 X-Intercept None 15.5 Y-Intercept y = 1 15.6 Horizontal Asymptote X ▯ axis : x ! 1 15.7 Increasing One ▯ to ▯ One 15.8 Points (0; 1) 6 (1; a) ▯ ▯ ▯1; 1 a 15.9 Graph Smooth Continuous No Corners No Gaps 16 Properties of f (x) = log x a 16.1 Domain All Positive Real Numbers 16.2 Range All Real Numbers 16.3 X-Intercept 1 16.4 Y-Intercept None 16.5 Vertical Asymptote Y ▯ Axis 7 (x = 0) 16.6 Decreasing 0 < a < 1 16.7 Increasing a > 1 16.8 Points (1; 0) (a; 1) ▯ ▯ 1; ▯1 a 16.9 Graph Smooth Continuous No Corners No Gaps 17 Property of Exponents 17.1 If...then... u v If : a = a Then : u = v 8

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