Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 49. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | Exploratory Problem for Chapter 13 461 26. ex - 2 3 27. 3ln x 5x 28 .- 5 13 29- . 2 - 1 10 3 . 27 31. 3 32. ln x - 3 - ln 2x 1 1 In Problems 33 throuogh 36 solve for x Q R and S are positive constants. 33. a 35x 2 100 b Q2x 1 R 34. a 2Qx 5 R b 2Q x 5 R 35. a Q R x S b QR x S 36. a R-x 1 - Q S b - S R 37. Acidity is determined by the concentration of hydrogen ions in a solution. The pH scale proposed by Sorensen in the early 1900s defines pH to be - log H where H is the concentration of hydrogen ions given in moles per liter. A pH of 7 is considered neutral a pH greater than 7 means the solution is basic while a pH of less than 7 indicates acidity. a If the concentration of hydrogen ions in a solution is increased tenfold what happens to the pH b If a blood sample has a hydrogen ion concentration of x 10-8 what is the pH c You ll find that the blood sample described in part b is mildly basic. Which has a higher concentration of hydrogen ions the blood sample or something neutral How many times greater is it In Problems 38 through 44 find all x for which each equation is true. 38. log x 3 log x3 39. ex3 ex 3 462 CHAPTER 13 Logarithmic Functions 40. In x 1 j 41. ln x - ln2 42. ex 1 ex e1 43. 102x 10210x 44 lnX 2 ln x 45. Suppose M0 is put in a bank account where it grows according to 12t r M t M0 1 12 where t is in years. a If r how long will it take for the amount of money in the account to increase by 50 b If the money doubles in exactly 8 years what is r 46. Find the equation of the straight line through the points 2 ln 2 and 3 ln 3 . 47. Find the equation of the line through the points 2 ln 2 and 2 e ln 2 e . 48. The Rule of 70 says that if a quantity grows exponentially at a rate of r per unit of time then its doubling time is usually about 70 r. This is merely a rule of thumb. Now we will determine how accurate an estimate this is and for what values of r it should be applied. Suppose that a quantity Q grows exponentially at r per unit of time t. Thus
