Answer Key
789
⎛ ⎝ log211 log0.5
⎞ ⎠
≈ −7.7211
295 .
⎛ ⎝ log0.452 log0.2
⎞ ⎠
≈0.4934
297 .
299 . ~17, 491 301 . Approximately $131,653 is accumulated in 5 years. 303 . i. a. pH = 8 b. Base ii. a. pH = 3 b. Acid iii. a. pH = 4 b. Acid 305 . a. ~333 million b. 94 years from 2013, or in 2107 307 . a. k ≈0.0578 b. ≈92 hours 309 . The San Francisco earthquake had 10 3.4 or ~2512 times more energy than the Japan earthquake. Review Exercises
311 . False 313 . False 315 . Domain: x >5, range: all real numbers
317 . Domain: x >2 and x < −4, range: all real numbers 319 . Degree of 3, y -intercept: 0, zeros: 0, 3−1, −1− 3 321 . cos 2 x – sin 2 x =cos2 x or = 1 – 2sin 2 x 2 or = 2cos
2 x – 1 2
323 . 0, ±2 π 325 . 4 327 . One-to-one; yes, the function has an inverse; inverse: f −1 ( x ) = 1 y 329 . x ≥ − 3 2 , f −1 ( x ) = − 3 2 + 1 2 4 y −7 331 . a. C ( x ) =300+7 x b. 100 shirts 333 . The population is less than 20,000 from December 8 through January 23 and more than 140,000 from May 29 through August 2 335 . 78.51% Chapter 2 Checkpoint 2.1 . 2.25 2.2 . 12.006001 2.3 . 16 unit 2 2.4 . lim x →1 1 x −1 x −1 =−1 2.5 . lim x →2 h ( x ) =−1. 2.6 . lim x →2 | x 2 −4 | x −2 does not exist. 2.7 . a. lim x →2 − | x 2 −4 | x −2 =−4; b. lim x →2 + | x 2 −4 | x −2 =4 2.8 . a. lim x →0 − 1 x 2 =+∞; b. lim x →0 + 1 x 2 =+∞; c. lim x →0 1 x 2 =+∞ 2.9 . a. lim x →2 − 1 ( x −2) 3 =−∞; b. lim x →2 + 1 ( x −2) 3 =+∞; c. lim x →2 1 ( x −2) 3 DNE. The line x =2 is the vertical asymptote of f ( x ) =1/( x −2) 3 . 2.10 . Does not exist. 2.11 . 11 10 2.12 . −13;
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