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Question : The half-life of a certain radioactive substance is 10 years. Suppose : 2163608

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the indicated composite for the pair of functions.

81) f(x) = 8.6(0.89)^{x}

A) C = 7.654;

a = 1.89;

R = 11%

B) C = 8.6;

a = 0.89;

R = -11%

C) C = 7.654;

a = 0.89;

R = -11%

D) C = 8.6;

a = 1.89;

R = 189%

If P dollars are deposited in an account paying R percent annual interest, approximate the amount in the account after x years.

82) P = $19,000, R = 9%, x = 8 years

A) $37,858.69

B) $30,970.00

C) $34,732.74

D) $32,680.00

83) P = $560, R = 9%, x = 16 years

A) $2039.79

B) $1316.00

C) $1366.40

D) $2223.37

The amount P is deposited in an account giving R% annual interest compounded n times a year. Find the amount A in the account after t years.

84) P = $4000, R = 10%, n = 4, t = 1

A) $4415.25

B) $4862.03

C) $4203.78

D) $5856.40

85) P = $19,000, R = 5%, n = 2, t = 5

A) $24,321.61

B) $23,750.00

C) $24,249.35

D) $21,496.76

86) P =$4200, R = 6%, n = 4, t = 5

A) $4876.97

B) $7585.67

C) $13,469.97

D) $5656.79

87) P = $1710, R = 8%, n = 365, t = 8

A) $3222.56

B) $3202.80

C) $3165.09

D) $3242.75

88) P = $6000, R = 8.5%, n = 2, t = 5

A) $7388.08

B) $9021.94

C) $9136.77

D) $9097.29

Evaluate f(x) at the given value of x. Approximate the answer to the nearest hundredth.

89) e^{x}, x = 3.1

A) 22.2

B) 24.53

C) 0.47

D) 1.13

90) e^{x}, x = 2

A) 8.17

B) 5.44

C) 7.39

D) 0.69

Graph the function in the window [-4, 4, 1] by [0, 8, 1]. State whether it illustrates exponential growth or exponential decay.

91) f(x) = 2e^{0.7x}

A) Growth

B) Decay

92) f(x) = e^{0.6x} + 2

A) Growth

B) Decay

93) f(x) = 1.8e^{-1.4x}

A) Decay

B) Growth

94) f(x) = 2.1e^{-x} + 2

A) Growth

B) Decay

Solve the problem.

95) The amount of particulate matter left in solution during a filtering process decreases by the equation P(n) = 700(0.5)^{0.8n}, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

A) 1400; 44

B) 700; 44

C) 700; 22

D) 700; 11,200

96) The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by D(x) = 4000(3)^{x}, where x is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at x = 0 and x = 5.

A) 12,000; 972,000

B) 4000; 108,000

C) 4000; 972,000

D) 4000; 60,000

97) The number of bacteria growing in an incubation culture increases with time according to B(x) = 5100(5)^{x}, where x is time in days. Find the number of bacteria when x = 0 and x = 2.

A) 5100; 15,937,500

B) 5100; 51,000

C) 5100; 127,500

D) 25,500; 127,500

98) The half-life of Cesium 134m is 3.0 hours. If the formula P(t) = ((1/2))^{t/3.0} gives the percent (as a decimal) remaining after time t (in hours), sketch P versus t.

A)

B)

C)

D)

99) A computer is purchased for $4600. Its value each year is about 79% of the value the preceding year. Its value, in dollars, after t years is given by the exponential function V(t) = 4600(0.79)^{t}. Find the value of the computer after 6 years. Round to the nearest cent.

A) $697.87

B) $21,804.00

C) $1118.20

D) $883.38

100) The half-life of a certain radioactive substance is 10 years. Suppose that at time t = 0 , there are 29 g of the substance. Then after t years, the number of grams of the substance remaining will be N(t) = 29((1/2))^{t/20}. How many grams of the substance will remain after 80 years? Round to the nearest hundredth when necessary.

A) 0.45 g

B) 1.81 g

C) 0.23 g

D) 0.91 g