Find P(x), the profit function.

A ceramics store manufactures and sells coffee mugs. The revenue r(x) from the sale of x coffee mugs is given by r(x)=6.5x. Suppose the function for the cost of manufacturing x coffee mugs is c(x)=0.75x+1850. a. Write the profit function. b. Find the profit on 500,1000, and 5000 coffee mugs.

The linear function f(x) = 48.8x + 63.8 models the number of smartphones sold in some country, f(x), in millions, x years after 2006. Find the slope of the model. Then describe what this means in terms of the rate of change of the dependent variable per unit change in the independent variable. The slope of the model is . (Type an integer or a decimal.)

The supply for a particular item is given by the function S(x) = 17 + 0.36x² . Find the producer's surplus if the equilibrium price of a unit $53. The producer's surplus is $