Exam 15: Integration

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The marginal revenue function for a manufacturer's product is given by = .Determine the demand equation for the product.

Determine: dx

The rate of growth of a bacteria (in thousands)is estimated by = 73t - 21,where t is in hours.If then find N(t).

The acceleration of an object after t seconds is given by y'' = 5t - 6,the velocity at 4 seconds is given by and the position at 1 second is given by Find y(t).

Determine:

The marginal price for a weekly demand of x bottles of shampoo is given by p'(x)= .Find p(x).

Use differentials to approximate .

Determine:

Determine:

If y = x ln x,then dy =

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If the marginal revenue for a manufacturer's product is = 700 - 6q - 8 ,find the demand function.

Suppose = 9; = 4,then find .

The supply equation for a certain radio is given by p = 0.8 + 17 where p is the price in dollars and x is the number of radios supplied.Use differentials to approximate the price when 620 radios are supplied.(Hint: Use x = 625.)

A managerial service determines that the rate of increase in maintenance costs (in dollars per year)for a particular house is given by M'(x)= 2x(3 + 70),where x is the age of the house in years and M(x)is the total (accumulated)cost of maintenance for x years.Find the total cost for the first 3 years.

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Determine:

If the marginal cost (in dollars)for a company is C'(x)= 200,and the cost for producing 8 units is $2250,that is C(8)= 2250,then find C(x).

A bacteria population is increasing at a rate of = 2 .Find p as a function of t.