25. No.  f (x);   For any real number n, real number b > 0, and function f (x) x = b , the graph of  ( 1 9. domain: all real numbers; range...View 9. since you will see how Shaun Dychko made the calculation. 23. 39. x = 4;   6 a. $35, 838.76 = 1  or x = −1 = 703, 800, 000 × ln(0.8) ln(0.5) years ≈ 226, 572, 993 years. x−3 The only difference is that "College Physics" omits the "Test Prep Domain:  (1, ∞) ;   Range:  (−∞, ∞) ;   Vertical asymptote: x → ∞ x-intercept:  ( = 1;   DNE In the expressions given, the base b  has the same value. 6.1 Section Exercises y = x , so it appears that they are inverse functions. 17/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax Rewriting as an exponential equation and solving for x 23. C b 23. logy 39 ( 100 ) = x 25. ln(h) = k 27. x −3 29. x 3. y = 0.25(3) 15. No solution To set up or model a linear equation to fit a real-world application, we must first determine the known quantities and define the unknown quantity as a variable. 3 log(y) ) The screencast video solutions here are second to none. C 6.8 Section Exercises This is a distance problem, so we can use the formula [latex]d=rt[/latex], where distance equals rate multiplied by time. n logb (x). − 55. x ≈ −0.472 As x → −∞ , f (x) → ∞ 2 S 47. f (−1) ≈ −0.2707 5 1 = log (6)−log (11) 13. These textbooks are available for free by following the links 6.5 Logarithmic Properties Find the dimensions of a rectangle given the area. 3. C Translate into algebra… 2   − The perimeter formula is standard: [latex]P=2L+2W[/latex]. 47, 622  fox x 9. The pH increases by about 0.301. Only the final exam remains, and the maximum of points that can be earned is 100. 0.151 1. exponential decay; The growth factor, 0.825, is between 0 and 1. 5. 2 3 = 9  3 2 (11) = 7. 9. Sample response: For a number of years, the population of forest A will increasingly After t = 20  years, forest A will have 43 more trees than forest B. The 19. plug it into your calculator. If the average number of minutes used each month is 420, then Company A offers a lower monthly cost of $55 compared to Company B’s monthly cost of $56.80. 2 The answer should be very close to 39. f (t) = 256e(0.068110t) ;  doubling time: about 10 minutes 4 ≈ 3.2 59. (x−3) x+2−6x+18 √2 )  2 or  ln ( 11 ) ) = − 3 1 −  ) 1 6.026 hours If spending continues at this rate, the graduate’s credit card debt will be $4,499.38 after one year. Josh is hoping to get an A in his college algebra class. 6. 14.125 17. logc (k) = d = $13,693 47. f (x) = 0.82 25.081 – x Company A charges a monthly service fee of $34 plus $.05/min talk-time. 3 19. Write a linear equation that models two different cell phone packages. As these amounts do not change, we call them fixed costs. x−3 S A linear equation can be used to solve for an unknown in a number problem. As both perimeter and area use length and width as dimensions, they are often used together to solve a problem such as this one. . The one-to-one property cannot be used when each side of the equation cannot be Next graph the scatter plot using the STAT PLOT feature. 12. 3 e x − 2;   the domain is  (−∞, ∞) ;   the range is  (−∞, −2) ;   the horizontal asymptote is  y = −2. 2 45. T (t) = 90e(−0.008377t) + 75, where t  is in minutes. 37. y = 5.063 + 1.934log(x) x−4  0 =  x = 4 x−3 Checking, we find that log6 (4 + 2) − log6 (4 − 3) = log6 (6) − log6 (1)   is defined, so x You won't make these kinds of mistakes 9. AP Courses" section found only in the "College Physics for AP These are examples of applications we come across every day that are modeled by linear equations.

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