# Functions

1. The number of cubic yards of dirt, D, needed to cover a garden with area a square feet is given by .
1. A garden with area 5000 ft2 requires 50 cubic yards of dirt. Express this information in terms of the function g.
2. Explain the meaning of the statement .

1. Select all of the following graphs which represent y as a function of x.

1. For each pair of functions  and  find  and
1.  and

1. Write the following as a composition of two functions.

1. The supply in thousands of items, for custom phone cases can be modeled by the equation , while demand can be while the demand can be modeled by , where p is in dollars.  Find the equilibrium price and quantity, the intersection of the supply and demand curves.

1. At a price of \$1.94 per bushel, the supply of corn is 9,800 million bushels and the demand is 9,300 million bushels. At a price of \$1.82 per bushel, the supply is 9,400 million bushels and the demand is 9,500 million bushels. What is the demand function?

1. The population of a certain city was 23,400 in 2002 and increased to 27,800 in the year 2006. If the population grew at a constant rate (that is, it grew linearly) write the equation for the population as a function of time.  ( Use the year 2002 corresponds to t = 0)

1. Working as an insurance salesperson, Ilya earns a base salary and a commission on each new policy, so Ilya’s weekly income, II, depends on the number of new policies, n, he sells during the week. Last week he sold 3 new policies, and earned \$760 for the week. The week before, he sold 5 new policies, and earned \$920. Find an equation for I(n), and interpret the meaning of the components of the equation.

1. A manufacturer can produce tires at a cost of \$20 apiece. It is estimated that is the tires are sold for  dollars apiece, consumers will buy  of them each month.  Express the manufacturer’s monthly profit as a function of price, graph the function, and use the graph to determine the optimal selling price.  How many tires will be sold each month at the optimal price?

1. Suppose that when the price of a certain commodity is dollars per unit, then hundred units will be purchased by consumers, where  . The cost of producing hundred units is   hundred dollars is  hundred dollars
1. Express the profit obtained from the sale of  hundred units as a function of    Sketch the graph of the profit function.
2. Use the profit curve found in part (a) to determine the level of production that results in maximum profit. What unit price p corresponds to maximum profit

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