65. Physics The function T ( t ) = T r + ( T i − T r ) e k t t open t close equals , t sub r , plus open , t sub i , minus , t sub r , close , e super k t end super  models Newton's Law of Cooling. T(t) is the temperature of a heated substance t minutes after it has been removed from a heat (or cooling) source. T i t sub i  is the substance's initial temperature, k is a constant for that substance, and T r t sub r  is room temperature.
    1. The initial surface temperature of a beef roast is 236°F and room temperature is 72°F. If k = − 0.041 , k equals negative , 0.041 , comma  how long will it take for this roast to cool to 100°F?
    2. Graphing Calculator Write and graph an equation that you can use to check your answer to part (a). Use your graph to complete the table below.

Standardized Test Prep

GRIDDED RESPONSE

SAT/ACT

66. An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What percent is the interest rate?
67. What is log 33 , 000 − log 99 + log 30 ? log , 33 comma 000 minus log , 99 plus log , 30 question mark
68. If f ( x ) = 5 − x 2 and g ( x ) = x 2 − 3 , f open x close equals 5 minus , x squared , and g open x close equals , x squared , minus 3 comma  what is ( g ∘ f ) ( 6 ) ? open g composition f close open 6 close question mark
69. What is the positive root of y = 2 x 2 − 35 x − 57 ? y equals 2 , x squared , minus 35 x minus 57 question mark
70. What is the real part of 3 + 2 i ? 3 plus , 2 to the i , question mark
71. What is 36 4 ? fraction square root of 36 , over square root of 4 end fraction , question mark

Mixed Review

See Lesson 7-5.

Solve each equation.

72. 3 2 x = 6561 3 super 2 x end super , equals , 6561
73. 7 x − 2 = 252 7 to the x , minus 2 equals 252
74. 25 2 x + 1 = 144 25 super 2 x plus 1 end super . equals 144
75. log 3 x = 4 log 3 x equals 4
76. log 5 x + 3 = 3.7 log 5 x plus 3 equals 3.7
77. log 9 − log x + 1 = 6 log 9 minus log x plus 1 equals 6

See Lesson 6-7.

Find the inverse of each function. Is the inverse a function?

78. y = 5 x + 7 y equals 5 x plus 7
79. y = 2 x 3 + y equals , 2 x cubed , plus  10
80. y = − x 2 + 5 y equals negative , x squared , plus 5
81. y = 3 x + 2 y equals 3 x plus 2

Get Ready! To prepare for Lesson 8-1, do Exercises 82–84.

See Lesson 2-2.

For Exercises 82–84, y varies directly with x.

82. If x = 2 x equals 2  when y = 4 , y equals 4 comma  find y when x = x equals  5.
83. If x = 1 x equals 1  when y = 5 , y equals 5 comma  find y when x = x equals  3.
84. If x = x equals  10 when y = 3 , y equals 3 comma  find y when x = 4. x equals 4.

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