#### 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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