Reference no: EM132848095

Assignment - Solve the problems.

1) Suppose that the daily cost in dollars of producing x televisions is C(x) = 0.003x³ + 0 1x² + 71x + 540 and currently 40 televisions are produced daily. Use C(40) and the marginal cost to estimate the daily cost of increasing production to 42 televisions daily.

2) The weekly profit, in dollars from the production and sale of x bicycles is given by P(x) = 10.00x - 0.005x². Currently, the company produces and sells 1300 bicycles per week. Use the marginal profit to estimate the change in profit if the company produces and sells one more bicycle per week.

3) A company estimates that the daily revenue (in dollars) from the sale of x cookies is given by R(x) = 815 + 0.05x + 0.0004x². Currently, the company sells 230 cookies per day. Use marginal revenue to estimate the increase in revenue if the company increases sales by one cookie per day.

4) The city of New Plains had a population of 13,000 in 2012 (t = 0) with a continuous growth rate of 1.25% per year.

a) Write the differential equation with the initial condition, that represents P(t), the population of New Plains after t years.

b) Find the particular solution of the differential equation from part (a).

c) Find P(10) and P'(10). Round to the nearest tenth as needed.

d) Find P'(10)/P(10), and explain what this number represents. Round to the nearest tenth as needed.