1. Graph these functions using graphing calculator. Then record your result. What pattern/conclusion/generalization can you make from these functions.

Transcription

1 MAC1105, Class Work (Eponential & Logarithmic Functions), Susan Sun Nunamaker Student's Name: 1. Graph these functions using graphing calculator. Then record your result. What pattern/conclusion/generalization can you make from these functions. A. f ( ) B. f ( ) 3 C. f ( ) 4 D. f ( ) ( 1 ) E. f ( ) ( 1 ) 3 F. f ( ) ( 1 ) 4 G. f ( ) 5 H. f ( ) 4 I. f ( ) 3 J. f ( ) 5 K. f ( ) 4 L. f ( )

2 . What is e? What equation/function is this value based on? 3. Find each of the following, to four decimal places. A. e 4 B. e C. e. D. e Sales of Packard Bell computers have grown eponentially in recent years. The t total revenue R, in billions, is given by R( t) ( 1. 4 ), such that t the number of years since A. Find the total revenue in 1990, 1994, 1996, 1997, 1998, 003, and 004. B. Graph the function. C. When will revenues be $8 billion?

3 5. Find each of the following. Do not use any calculator. A. log 16 B. log 3 9 C. log 5 15 D. log 64 E. log F. log100 G. log 1 4 H. log 8 I. ln1 J. ln e K. log10 L. log1 6. Convert to a logarithmic equation.do not use any calculator. A B t C. Q D. e E. p k 3 F. e 3 t 7. Convert to an eponential equation. No need for calculator. A. log B. t log 4 7 C. log D. log E. ln F. ln

4 8. Find the logarithm using the change-of-base formula. You may use a calculator. A. log B. log 3 0 C. log D. log E. log 104 F. log G. log H. log I. log J. log The loudness L, in bels (after Aleander Graham Bell), of a sound of intensity I I is defined to be L log such that I 0 = the minimum intensity detectable by the I 0 human ear (such as the tick of a watch at 0 ft under quiet conditions). If a sound is 10 times as intense as another, its loudness is 1 bel greater than that of the other. If a sound is 100 times as intense as another, its loudness is bels greater, and so on. The bel is a large unit, so a subunit, the decibel, is generally used. For L, in I decibels, the formula is L 10log. Find the loudness, in decibels, of each sound I 0 with the given intensity. SOUND INTENSITY A. Library 510I 0 B. Conversational speech 10 6 I 0 C. Heavy truck 10 9 I 0 4

5 10. Epress each as the logarithm of a single quantity A. log a log c B. log 9 log 4 b b 5 5 C. 3log e 4log e n D. 1 log b a log 5 b E. log10 5 3log10 log10 y F. 1 ln( 3 5) ln Find the balance A for P dollars invested at rate r for t years, compounded n times per y ear: A. P $ 1000, r 10%, t 10 years, n 1 B. P $ 1000, r 10%, t 40years, n C. P $ 1000, r 10%, t 40years, n 4 D. P $ 1000, r 8%, t 40years, n 5

6 E. P $ 1000, r 8%, t 10years, n F. P $ 800, r 8%, t 10years, n 1. Use the property of logarithms to write the epression as a sum, difference, and/or multiple of logarithms. A. log 6 6 B. log 5 C. log 3 z D. ln t E. ln( ) 3 F. log b z Solve for : 1 A. 64 B. 4 C D. log 5 5 E. ln( 1) 0 F. e 5 G. 5e 47 H. e 6 38 I. 3e 14 6

7 J. e 6e 8 0 K. 80e 0 70 L e M. ln 3 N. ln 4. 5 O. 3ln 1 P. 3ln 5 10 Q. 6 ln 3 0 R. ln 1 S. ln ln( ) 3 T. ln ( ) Find the time required for a $1000 investment to double at interest rate of r , compounded continuously. (Hint: A Pe rt for continuous compounding ) 15. Find the time required for a $1000 investment to triple at interest rate of r , compounded continuously. (Hint: A Pe rt for continuous compounding ) 7

8 16. The population P of a city is given by P 5, 000e kt where t is the time in years, with t 0 corresponding to In 1945, the population was Find the value of k and use this result to predict the population in the year The number of bacteria N in a culture is given by the model N 100e kt where t is the time in hours, with t 0 corresponding to time when N 100. When t 4, there are 50 bacteria. How long does it take the population to double in size? To triple in size? 8

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