Understanding Exponential and Logarithmic Functions: Growth Models and Graphs

C H A P T E R 4 Exponential andLogarithmic Functions

Figure 4.1 Two models for population growth. 4-1-112

Figure 4.2 The graphs of fourexponential functions. 4-1-113

Figure 4.3 Typical exponential graphs. 4-1-114

Figure 4.4 Exponential change. 4-1-115

Figure 4.5 Reflection of points acrossthe line y = x. 4-2-116

Figure 4.6 The graph of y = ln x is the reflection of the graph of y = ex across the line y = x. 4-2-117

Figure 4.7Equality rule: Since the graph of y = ln x always rises, a b implies ln a  ln b. 4-2-118

Figure 4.8 At each point P(c, ec) on the graphy = ex, the slope equals ec. 4-3-119

Figure 4.9 Revenue R = 5.000pe–0.02p. 4-3-120

Figure 4.10 The standard normal density function: 4-4-121

Figure 4.11 The graph of f(x) = x2 – 8 ln x. 4-4-122

Figure 4.12 Present value 4-4-123

Figure 4.13 A learning curve Q(t) = B – Ae–kt. 4-4-124

Figure 4.14 Worker efficiency Q(t) = 700 – 400e–0.05t. 4-4-125

Figure 4.15 A logistic curve 4-4-126

Figure 4.16 The spread of an epidemic 4-4-127

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