COMPOUND INTEREST Complete the table for the time (in

Chapter , Problem 29

(choose chapter or problem)

COMPOUND INTEREST Complete the table for the time (in years) necessary for dollars to triple if interest is compounded annually at rate 30. MODELING DATA Draw a scatter plot of the data in Exercise 29. Use the regression feature of a graphing utility to find a model for the data. 31. COMPARING MODELS If $1 is invested in an account over a 10-year period, the amount in the account, where represents the time in years, is given by or depending on whether the account pays simple interest at or continuous compound interest at 7%. Graph each function on the same set of axes. Which grows at a higher rate? (Remember that is the greatest integer function discussed in Section 2.4.) 32. COMPARING MODELS If $1 is invested in an account over a 10-year period, the amount in the account, where represents the time in years, is given by or depending on whether the account pays simple interest at 6% or compound interest at compounded daily. Use a graphing utility to graph each function in the same viewing window. Which grows at a higher rate? RADIOACTIVE DECAY In Exercises 3338, complete the table for the radioactive isotope. Half-life Initial Amount After Isotope (years) Quantity 1000 Years 33. 1599 10 g 34. 5715 6.5 g 35. 24,100 2.1 g 36. 1599 2 g 37. 5715 2 g 38. 24,100 0.4 g In Exercises 3942, find the exponential model that fits the points shown in the graph or table. 39. 40. 41. 42. 43. POPULATION The populations (in thousands) of Horry County, South Carolina from 1970 through 2007 can be modeled by where represents the year, with corresponding to 1970. (Source: U.S. Census Bureau) (a) Use the model to complete the table. (b) According to the model, when will the population of Horry County reach 300,000? (c) Do you think the model is valid for long-term predictions of the population? Explain. 44. POPULATION The table shows the populations (in millions) of five countries in 2000 and the projected populations (in millions) for the year 2015. (Source: U.S. Census Bureau) (a) Find the exponential growth or decay model or for the population of each country by letting correspond to 2000. Use the model to predict the population of each country in 2030. (b) You can see that the populations of the United States and the United Kingdom are growing at different rates. What constant in the equation is determined by these different growth rates? Discuss the relationship between the different growth rates and the magnitude of the constant. (c) You can see that the population of China is increasing while the population of Bulgaria is decreasing. What constant in the equation reflects this difference? Explain. y aebt y aebt t 0 y aebt y aebt t t 0 P 18.5 92.2e0.0282t P x 1234 2 4 6 8 (4, 5) ( ) 1 2 0, y x 12345 2 4 6 8 10 (3, 10) (0, 1) y y aebx 239Pu 14C 226Ra 239Pu 14C 226Ra 5 1 2% A 1 0.055 365 365t A 1 0.06 t t t 7 1 2% A e0.07t A 1 0.075t t r. t P r