Chapter 8

Recommendations

Info

8.7 Solution D(n) 5 (1 2 0.022) n Write an exponential model, using D(n) to represent the percent of dye remaining as a decimal and n to represent the number of washings. D(n) 5 (0.978) n Since the jeans are losing 2.2% of the dye each time, the ratio of decline is 0.978. 0.30 5 (0.978) n Replace D(n) with 0.30 since the well-worn look requires no more than 30% of the original dye remaining. log (0.30) 5 log (0.978) n log (0.3) 5 n log (0.978) To solve for n, take the log of both sides of the equation. Rewrite the equation with the power as a coefficient. log (0.3) log (0.978) 5 n Divide both sides of the equation by log (0.978) to solve for n. 54.12 8 n It would take about 54 washings to give the jeans a well-worn look. EXAMPLE 4 Solving a problem about sound intensity using logarithms The dynamic range of human hearing and sound intensity spans from 10 212 W>m 2 to about 10 W>m 2 . The highest sound intensity that can be heard is 10 000 000 000 000 times as loud as the quietest! This span of sound intensity is impractical for normal use. A more convenient way to express loudness is a relative logarithmic scale, with the lowest sound that can be heard by the human ear, I 0 5 10 212 W>m 2 , given the measure of loudness of 0 dB. Recall that the formula that is used to measure sound is L 5 10 log Q I R , where L I0 is the loudness measured in decibels, I is the intensity of the sound being measured, and I 0 is the intensity of sound at the threshold of hearing. The following table shows the loudness of a selection of sounds measured in decibels. NEL <strong>Chapter</strong> 8 497
Solution Sound Loudness (dB) soft whisper 30 normal conversation 60 shouting 80 subway 90 screaming 100 rock concert 120 jet engine 140 space-shuttle launch 180 How many times more intense is the sound of a rock concert than the sound of a subway? L 5 10 log a I I 0 b 120 5 10 log a I RC I 0 b 90 5 10 log a I S I 0 b Let the intensity of sound for a rock concert be I RC and for a subway be I S . Find the values for the loudness of these sounds in the table, and substitute into the formula. 12 5 log a I RC I 0 b 9 5 log a I S I 0 b Divide both sides of the equations by 10. 10 9 5 I S 10 12 5 I RC I 0 I 0 10 12 I 10 9 0 5 I RC I 0 5 I S Express both equations in exponential form. Isolate the variables for comparison. I RC I S 5 1012 I 0 10 9 I 0 5 10 3 5 1000 Divide the results to compare the sound of a rock concert with the sound of a subway. The sound of a rock concert is 1000 times more intense than the sound of a subway. 498 8.7 Solving Problems with Exponential and Logarithmic Functions NEL
Page 1 and 2:
444 NEL
Page 3 and 4: 8 Getting Started Study Aid • For
Page 5 and 6: 8.1 Exploring the Logarithmic Funct
Page 7 and 8: In Summary Key Ideas • The invers
Page 9 and 10: 8.2 Transformations of Logarithmic
Page 11 and 12: Reflecting L. Describe the domain a
Page 13 and 14: EXAMPLE 2 Connecting a geometric de
Page 15 and 16: PRACTISING 4. Let f (x) 5 log 10 x.
Page 17 and 18: Solution B: Using a graphing calcul
Page 19 and 20: c) log 2 (24) 5 x Determine the exp
Page 21 and 22: EXAMPLE 4 Selecting a strategy to e
Page 23 and 24: CHECK Your Understanding 1. Express
Page 25 and 26: 17. The doubling function y 5 y 0 2
Page 27 and 28: log a (mn) 5 x 1 y m 5 a x so log a
Page 29 and 30: APPLY the Math EXAMPLE 4 Selecting
Page 31 and 32: EXAMPLE 6 Selecting strategies to s
Page 33 and 34: 9. Write each expression as a singl
Page 35 and 36: Study • See Lesson 8.2, Examples
Page 37 and 38: 8.5 Solving Exponential Equations G
Page 39 and 40: Solution C: Solving the equation gr
Page 41 and 42: EXAMPLE 4 Solve 2 x11 5 3 x21 to th
Page 43 and 44: 8. Solve for x. a) 4 x11 1 4 x 5 16
Page 45 and 46: Reflecting A. What strategies for s
Page 47 and 48: x 2 2 9 5 2 4 x 2 2 9 5 16 x 2 5 25
Page 49 and 50: 9. The loudness, L, of a sound in d
Page 51 and 52: APPLY the Math EXAMPLE 1 Solving a
Page 53: EXAMPLE 2 Representing exponential
Page 57 and 58: 6. Calculate to two decimal places
Page 59 and 60: 8.8 Rates of Change in Exponential
Page 61 and 62: EXAMPLE 2 Selecting a strategy for
Page 63 and 64: Solution -2 Tangents to y = 10 x y
Page 65 and 66: y 8 y = log x - 1 6 2 d 4 2 y = - 1
Page 67 and 68: PRACTICE Questions Lesson 8.1 1. De
Page 69 and 70: 8 Chapter Self-Test 1. Write the eq
Page 71 and 72: 2(sec 2 x 2 tan 2 x) 9. 5 sin 2x se
Page 73 and 74: d) D 5 5xPR 0 x . 06, R 5 5 yPR6 e)
Page 75 and 76: 17. log b x!x 5 log b x 1 log b !x
Page 77: value of x. Determine the average r
show all

Chapter 8

Create successful ePaper yourself

Delete template?

Save as template?