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Question : A company determines that its marginal revenue (in dollars per day) is given : 2151786

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

Find the area between the curves.

1) y = 2x - x^{2}, y = 2x - 4

A) (37/3)

B) (32/3)

C) (31/3)

D) (34/3)

2) y = x^{2} - 5x + 4, y = -(x - 1)^{2}

A) (8/7)

B) (9/8)

C) (8/9)

D) (7/8)

3) x = 0, x = -2, y = e^{x}, y = 0

A) e^{-2} - 1

B) 1 - e^{-2}

C) e^{-2}

D) 1 + e^{-2}

4) y = x^{3}, y = 4x

A) 16

B) 8

C) 2

D) 4

5) y = x, y = x^{2}

A) (1/2)

B) (1/6)

C) (1/3)

D) (1/12)

6) x = 0, x = 1, y = x^{2} + 6, y = x^{2} + 2

A) 12

B) 8

C) 16

D) 4

7) y = x^{2}, y = 4

A) (31/3)

B) (37/3)

C) (34/3)

D) (32/3)

8) y = (1/2)x^{2}, y = -x^{2} + 6

A) 8

B) 4

C) 16

D) 32

9) y = x^{3}, y = x^{2}

A) (1/6)

B) (5/6)

C) (1/12)

D) (5/12)

10) x = 2, x = 5, y = (1/x), y = (1/x^{2})

A) ln(5/2) - (1/10)

B) ln(5/2) + (1/10)

C) ln(5/2) - (3/10)

D) ln(5/2) + (3/10)

11) x = 1, x = 6, y = lnx , y = ln2x

A) ln32

B) ln64

C) ln2

D) ln32 - 10

12) x = -4, x = 4, y = 2x/(1 + x^{2}), y = 0

A) 2 e^{17}

B) 2 ln17

C) 0

D) ln17

Solve the problem.

13) Find the producers' surplus if the supply function is given by S(q) = q^{2} + 4q + 20. Assume supply and demand are in equilibrium at q = 24.

A) 10,386

B) 10,368

C) 10,836

D) 10,638

14) Find the producers' surplus if the supply function of some item is given by S(q) = q^{2} + 2q + 8. Assume supply and demand are in equilibrium at q = 30.

A) 19,800

B) 18,900

C) 17,200

D) 12,700

15) Find the consumers' surplus if the demand function for an item is given by D(q) = 30 - q^{2}, assuming supply and demand are in equilibrium at q = 4.

A) 128

B) (64/3)

C) (128/3)

D) 64

16) Find the consumers' surplus if the demand for an item is given by D(q) = 72 - q^{2}, assuming supply and demand are in equilibrium at q = 6.

A) 72

B) 144

C) 432

D) 216

17) Suppose the supply function of a certain item is given by S(q) = 4q + 2, and the demand function is given by D(q) = 14 - q^{2}. Find the producers' surplus.

A) 8

B) 16

C) (8/3)

D) (16/3)

18) Suppose the supply function of a certain item is given by S(q) = 2q + 7, and the demand function is given by D(q) = 27 - q^{2/3}. Find the producers' surplus. (Hint: The equilibrium quantity q_{0}is a perfect cube.)

A) (32/5)

B) (64/5)

C) 32

D) 64

19) Suppose the supply function of a certain item is given by S(q) = 2q + 7, and the demand function is given by D(q) = 27 - q^{2/3}. Find the consumers' surplus. (Hint: The equilibrium quantity q_{0}is a perfect cube.)

A) (32/5)

B) 32

C) (64/5)

D) 64

20) Suppose the supply function of a certain item is given by S(q) = 2e^{q}, and the demand function is given by D(q) = 8e^{-q}. Find the producers' surplus. Round your answer to three decimal places.

A) 0.773

B) 1.337

C) 0.664

D) 1.228

21) Suppose the supply function of a certain item is given by S(q) = 2e^{q}, and the demand function is given by D(q) = 8e^{-q}. Find the consumers' surplus. Round your answer to three decimal places.

A) 0.773

B) 1.227

C) 1.337

D) 0.664

22) A company determines that its marginal revenue per day is given by R'(t) = 50e^{t}, and that R(0) = 0, where R(t) = revenue, in dollars, on the t^{th} day. The company's marginal cost per day is given by C'(t) = 120 - 0.3t, and that C(0) = 0, where C(t) = cost, in dollars, on the t^{th} day. Find the total profit from t = 0 to t = 9 (the first 9 days). Round your answer to the nearest dollar.

Note: P(T) = R(T) - C(T) =

A) $404,036

B) $404,012

C) $404,086

D) $404,048

23) A company determines that its marginal revenue (in dollars per day) is given by MR(t) = 120e^{t}. The company's marginal cost (in dollars per day) is given by MC(t) = 50 - 0.2t. Find the total profit from t = 0 to t = 8 (the first 8 days).

A) $357,189

B) $357,201

C) $357,321

D) $357,208

24) The flow of blood in a blood vessel is faster toward the center of the vessel and slower toward the outside. The speed of the blood is given by V = (p/4Lv)(R^{2} - r^{2}), where R is the radius of the blood vessel, r is the distance of the flowing blood from the center of the blood vessel, and p, v, and L are physical constants related to the pressure and viscosity of the blood and the length of the blood vessel. If R is constant, we can think of V as a function of r: V(r) = (p/4Lv)(R^{2} - r^{2}). The total blood flow Q is given by Q(R) = . Find Q for a blood vessel of radius R = 1.4 mm.

A) (2401/3750) (πp/Lv)

B) (343/375) (πp/Lv)

C) (2401/5000) (πp/Lv)

D) (2401/2500) (πp/Lv)

25) In town A, the birth rate is given by b'(t) = 50e^{0.26t} (births per year), where t is the number of years since 1990. In town B, the birth rate is given by B'(t) = 80e^{0.30t} (births per year), where t is the number of years since 1990. How many more births are there in town B than in town A during the 1990s (from t = 0 to t = 10)?

A) 2767 births

B) 5089 births

C) 904 births

D) 2693 births

26) The velocity of particle A, t seconds after its release is given by v_{a}(t) = 9.8t - 0.5t^{2} meters per second. The velocity of particle B, t seconds after its release is given by v_{b}(t) = 11.4t - 0.3t^{2} meters per second. If velocity is measured in meters per second, how much farther does particle B travel than particle A during the first ten seconds (from t = 0 to t = 10)? Round to the nearest meter.

A) 4 m

B) 360 m

C) 147 m

D) 280 m

27) The velocity of particle A, t seconds after its release is given by v_{a}(t) = 3.3e^{0.5t} meters per second. The velocity of particle B, t seconds after its release is given by v_{b}(t) = 13.4t - 0.4t^{2} meters per second. If velocity is measured in meters per second, how much farther does particle A travel than particle B during the first ten seconds (from t = 0 to t = 10)? Round to the nearest meter.

A) 443 m

B) 303 m

C) 703 m

D) 436 m