SECTION 5.3 Exponential Functions 309 87. = − If4 7,whatdoes4 equal? x x2 88. If 2 3, whatdoes 4 equal? x x = − 89. = − If 3 2,whatdoes3 equal? x x2 90. If 5 3, what does 5 equal? x x3 = − 91. If = 9 25, x what does 3x equal? 92. If = −2 1 1000 , x3 what does 2x equal? In Problems 93–96, determine the exponential function whose graph is given. 93. x y 3 (0, 1) (1, 3) (2, 9) (–1, ) 20 4 8 12 16 –2 1 – 3 –3 –2 –1 1 2 y 5 0 94. x y 3 (1, 5) (0, 1) (–1, ) 20 4 8 12 16 –2 1 – 5 –3 –2 –1 1 2 y 5 0 95. x y –1 1 2 3 –10 –30 –20 –40 (–1, – ) 1 – 6 (2, –36) (1, –6) (0, –1) y 5 0 96. x y 3 2 –4 –12 –8 (–1, – ) 1 –e (2, –e2) (1, –e) (0, –1) y 5 0 98. Find an exponential function whose graph has the horizontal asymptote = − y 3 and contains the points ( ) − 0, 2 and ( ) −2, 1 . 97. Find an exponential function whose graph has the horizontal asymptote = y 2 and contains the points 0, 3 and 1, 5 . ( ) ( ) 99. Suppose that ( ) = f x 2 .x (a) What is ( ) f 4 ? What point is on the graph of f ? (b) If ( ) = f x 1 16 , what is x? What point is on the graph of f ? 100. Suppose that ( ) = f x 3 .x (a) What is ( ) f 4 ? What point is on the graph of f ? (b) If ( ) = f x 1 9 , what is x ? What point is on the graph of f ? 101. Suppose that ( ) = + g x 4 2. x (a) What is −g( 1)? What point is on the graph of g? (b) If ( ) = g x 66, what is x? What point is on the graph of g? 102. Suppose that ( ) = − g x 5 3. x (a) What is − g( 1)? What point is on the graph of g? (b) If ( ) = g x 122, what is x? What point is on the graph of g? 103. Suppose that ( ) ( ) = − H x 1 2 4. x (a) What is ( ) − H 6 ? What point is on the graph of H? (b) If ( ) = H x 12, what is x? What point is on the graph of H? (c) Find the zero of H. 104. Suppose that ( ) ( ) = − F x 1 3 3. x (a) What is ( ) − F 5 ? What point is on the graph of F? (b) If ( ) = F x 24, what is x? What point is on the graph of F ? (c) Find the zero of F. Applications and Extensions 109. Optics If a single pane of glass obliterates 3% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the function ( ) = ⋅ p n 100 0.97n (a) What percent of light will pass through 10 panes? (b) What percent of light will pass through 25 panes? (c) Explain the meaning of the base 0.97 in this problem. Mixed Practice In Problems 105–108, graph each function. Based on the graph, state the domain and the range, and find any intercepts. 105. f x e x e x if 0 if 0 x x ( ) = < ≥ ⎧ ⎨ ⎪ ⎩⎪⎪ − 106. f x e x e x if 0 if 0 x x ( ) = < ≥ ⎧ ⎨ ⎪ ⎩⎪⎪ − 107. f x e x e x if 0 if 0 x x ( ) = − < − ≥ ⎧ ⎨ ⎪ ⎩⎪⎪ − 108. f x e x e x if 0 if 0 x x ( ) = − < − ≥ ⎧ ⎨ ⎪ ⎩⎪⎪ −
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