MATT

1.  Given the demand function D(p)=100−3p^2,

Find the

Elastic

ity of Demand at a price of $4

 

At this price, we would say the demand is:

• Inelastic

Elastic

• Unitary

Based on this, to increase revenue we should:

• Raise Prices
• Keep Prices Unchanged
• Lower Prices

2.  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 

3.  Find ∫4e^xdx

  + C

 

4.  Find ∫(7x^6+6x^7)dx

  + C 

5.  Find ∫(7/x^4+4x+5)dx

  + C

6.  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?

  cars  

7.  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: $

8.  Evaluate the integral
∫x^3(x^4−3)^48dx
by making the substitution u=x^4−3.

  + C

NOTE: Your answer should be in terms of x and not u. 

9.  Evaluate the indefinite integral.

∫x^3(8+x^4)^1/2dx

  + C 

10.  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 .

11.  ∫4xe^6xdx =    + C 

12.  Find ∫6x/7x+5dx

  + C 

13.  Sketch the region enclosed by y=4x and y=5x^2. Find the area of the region.

14.  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 = 

15.  Suppose you deposit $1000 at 4% interest compounded continuously. Find the average value of your account during the first 2 years.

$
 

16.  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: $

17.  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: $

18.  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.

$
 

19.  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

R(x,y)=110x+170y−4x^2−2y^2−xy

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 =    
 

20.  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.