B Apply

46. Think About a Plan An earthquake of magnitude 9.1 occurred in 2004 in the Indian Ocean near Indonesia. It was about 74,900 times as strong as the greatest earthquake ever to hit Texas. Find the magnitude of the Texas earthquake. (Remember that an increase of 1.0 on the Richter scale means an earthquake is 30 times stronger.)
    • Can you write an exponential or logarithmic equation?
    • How does the solution of your equation help you find the magnitude?

47. Consider the equation 2 x 3 = 80 . 2 super x over 3 end super , equals 80 . .

    1. Solve the equation by taking the logarithm base 10 of each side.
    2. Solve the equation by taking the logarithm base 2 of each side.
    3. Writing Compare your result in parts (a) and (b). What are the advantages of each method? Explain.
48. Seismology An earthquake of magnitude 7.7 occurred in 2001 in Gujarat, India. It was about 4900 times as strong as the greatest earthquake ever to hit Pennsylvania. What is the magnitude of the Pennsylvania earthquake? (Hint: Refer to the Richter scale on page 453.)
49. As a town gets smaller, the population of its high school decreases by 6% each year. The senior class has 160 students now. In how many years will it have about 100 students? Write an equation. Then solve the equation without graphing.

Mental Math Solve each equation.

50. 2 x = 1 2 2 to the x , equals , 1 half
51. 3 x = 27 3 to the x , equals 27
52. log 9 3 = x log base 9 , 3 equals x
53. log 4 64 = x log base 4 , 64 equals x
54. log 8 2 = x log base 8 , 2 equals x
55. 10 x = 1 100 10 to the x , equals , 1 100th
56. log 7 343 = x log base 7 , 343 equals x
57. 25 x = 1 5 25 to the x , equals , 1 fifth
58. Demography The table below lists the states with the highest and with the lowest population growth rates. Determine in how many years each event can occur. Use the model P = P 0 ( 1 + r ) x , p equals , p sub 0 . open 1 plus r close to the x . comma  where P 0 p sub 0  is population from the table, as of July, 2007; x is the number of years after July, 2007, P is the projected population and r is the growth rate.
    1. Population of Idaho exceeds 2 million.
    2. Population of Michigan decreases by 1 million.
    3. Population of Nevada doubles.

SOURCE: U.S. Census Bureau

Table of Contents