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Findthemarginal profitwhenthevalueofxis 5 43

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Unformatted text preview: servoir held 200 million gallons of water, and on the 21st it held only 164 million gallons. a) Express the amount of water in the reservoir as a linear function of time. b) How much water was in the reservoir on the 8th of the month? 35) The profit in dollars from the sale of x thousand compact disc players is P(x) = x3 - 3x2 + 3x + 8. Find the marginal profit when the value of x is 5. 43) Suppose the cost of producing x units of a particular commodity is C(x) = 0.04x2 + 5x + 73 hundred dollars. a) Use marginal cost to estimate the cost of producing the sixth unit. b) What is the actual cost of producing the 6th unit? c) Use marginal cost to estimate the additional cost if the number of units produced increases from 5 to 5.25, 36) Find the equation of the tangent line to the curve y = 3x2 + 7x - 3 at the point where x = 1. Given the distance function, s(t), where s is in feet and t is in seconds, find the velocity function, v(t), and the acceleration function, a(t). 37) s(t) = t2 + 2t - 24 a) What is the velocity function? b) What is the acceleration function? c) What is the velocity at time t = 2? d) What is the acceleration when t = 2? e) At what time is the velocity equal to 30? 44) Suppose that t years from now the population of a town will be P(t) = - t3 + 9t2 + 48t + 200 where P is in thousands. a) At what rate will the population be growing 3 years from now? b) After how many years will the rate of growth be 63,000? 38) A stone is dropped from a height of 144 feet. Its height at any time t (seconds) is H(t) = - 16 t2 + 144 feet a) When will the stone hit the ground? b) What is the velocity of the stone when it hits the ground? 2 Answer Key Testname: M119‐REVIEW_CH‐0‐1 1) y = - 11 x + 4 5 15 5 2) y = - x + 7 7 8 68 3) y = - x + 9 9 4) y = - 3x - 13 5) t4/11 6) a - 11/3 7) (x3 + b)- 1/2 8) (x + 9)3/2 5 9) y7 10) 11) 12) 5 6 b2 1 d11 1 s 3 13) t14 14) 7 15) - 2 1 16) avg rate of change = instantaneous rate of change = 1 2 17) 2x + 1 + h 18) 4 19) 4x + 6 20) 20x3 - 27x2 21) - 34x- 3 + 12x2 + 10 63 2/5 x - 10x 22) 5 23) 64x3 + 72x2 + 18x 24) 6x5 + 36x3 + 54x = 6x(x2 + 3)2 25) 42x - 6 26) 980(7x - 6)3 6 27) 2 + x4 28) 187 8 29) 3 4 30) 2 31) y = - 4x- 1 32) (0, 0) and (12, - 276) 33) a) x2 + 5x+ 5 b) x2 + 3x+ 2 3 Answer Key Testname: M119‐REVIEW_CH‐0‐1 34) P(x) = 81x - 16600 35) \$48 36) y = 13x - 6 37) a)v(t) = 2t + 2; b) a(t) = 2 c) velocity at t =2 is 6 d) acceleration a t = 2 is 2 e) t= 14 38) a) 3 seconds b) - 96 ft/sec (the negative sign means the stone is coming down at the moment it hits the ground) 39) F = 2w + 7200/w 40) S.A. = 2x^2 + 6000/x 13.78 π 41) S.A. = 2πr2 + r 42) a) y = - 4t + 248 43) a) Cʹ(5) = \$540 44) a) 75,000 people per year b) 216 million gallons b) C(6) - C(5) = \$544 c) Cʹ(5)*.25 = \$135 b) at t= 1 year and t = 5 years 4...
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