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## Elasticity of Demand at a price

#### Elasticity of Demand at a price

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:

• 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.

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