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.
