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  1. Given the demand function D(p)=100−3p^2,
    Find the Elasticity of Demand at a price of $4

At this price, we would say the demand is:
Based on this, to increase revenue we should:
Raise Prices
Keep Prices Unchanged
Lower Prices

  1. Given that f'(x)=−5(x−5)(x+4),
    The graph of f(x)f(x) at x=3 is Select an answer increasing concave up increasing concave down decreasing concave up decreasing concave down
  2. Find ∫4e^xdx
  • C
  1. Find ∫(7x^6+6x^7)dx
  • C
  1. Find ∫(7/x^4+4x+5)dx
  • C
  1. The traffic flow rate (cars per hour) across an intersection is r(t)=200+600t−90t^2, where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6 am and 10 am?
  2. A company’s marginal cost function is 5/√x where x is the number of units.
    Find the total cost of the first 81 units (of increasing production from x=0 to x=81)
    Total cost: $
  3. Evaluate the integral
    by making the substitution u=x^4−3.
  • C
    NOTE: Your answer should be in terms of x and not u.
  1. Evaluate the indefinite integral.
  • C
  1. A cell culture contains 2 thousand cells, and is growing at a rate of r(t)=10e^0.23t thousand cells per hour.
    Find the total cell count after 4 hours. Give your answer accurate to at least 2 decimal places.
    _thousand cells .
  2. ∫4xe^6xdx = + C
  3. Find ∫6x/7x+5dx
  • C
  1. Sketch the region enclosed by y=4x and y=5x^2. Find the area of the region.
  2. Determine the volume of the solid generated by rotating function f(x)=(36−x^2)^1/2 about the x-axis on [4,6].
    Volume =
  3. Suppose you deposit $1000 at 4% interest compounded continuously. Find the average value of your account during the first 2 years.
  4. Given: (x is number of items)
    Demand function: d(x)=3362√x
    Supply function: s(x)=2√x

Find the equilibrium quantity: items
Find the consumers surplus at the equilibrium quantity: $

  1. Given: (x is number of items)
    Demand function: d(x)=3072/√x
    Supply function: s(x)=3√x
    Find the equilibrium quantity: items
    Find the producer surplus at the equilibrium quantity: $
  2. Find the accumulated present value of an investment over a 9 year period if there is a continuous money flow of $9,000 per year and the interest rate is 1% compounded continuously.
  3. A company manufactures 2 models of MP3 players. Let x represent the number (in millions) of the first model made, and let y represent the number (in millions) of the second model made.
    The company’s revenue can be modeled by the equation
    Find the marginal revenue equations
    Rx(x,y) =
    Ry(x,y) =
    We can achieve maximum revenue when both partial derivatives are equal to zero. Set Rx=0and Ry=0 and solve as a system of equations to the find the production levels that will maximize revenue.
    Revenue will be maximized when:
    x =
    y =
  4. An open-top rectangular box is being constructed to hold a volume of 200 in^3. The base of the box is made from a material costing 5 cents/in^2. The front of the box must be decorated, and will cost 11 cents/in^2. The remainder of the sides will cost 2 cents/in^2.
    Find the dimensions that will minimize the cost of constructing this box.
    Front width: in.
    Depth: in.
    Height: in.
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