- 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

- 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 - Find ∫4e^xdx

- C

- Find ∫(7x^6+6x^7)dx

- C

- Find ∫(7/x^4+4x+5)dx

- C

- 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 - 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: $ - 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.

- Evaluate the indefinite integral.

∫x^3(8+x^4)^1/2dx

- C

- 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 . - ∫4xe^6xdx = + C
- Find ∫6x/7x+5dx

- C

- Sketch the region enclosed by y=4x and y=5x^2. Find the area of the region.
- 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 = - Suppose you deposit $1000 at 4% interest compounded continuously. Find the average value of your account during the first 2 years.

$ - 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: $

- 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: $ - 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.

$ - 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 = - 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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