Functions and Exponents-Heart of Algebra

  1. Staples now sells their own notebooks. Making notebook has a fixed factory cost of$6,000 and a per unit cost of $0.58 per notebook. Staples sells these notebooks for $3.99 each.
    1. As a function of the number of notebooks staples sells (n), write an equation for Staples’ profit P(n).
    2. How many notebooks does Staples need to sell in order to make $7,500 in profit?
    3. Write Staples’ cost function for notebooks where C(n) is cost in terms of the number of notebooks Staples produces. What is the fixed cost and the variable cost?
    4. In 2013, Staples decided to sell these notebooks for $2.50 instead of $3.99. The company returned zero profit. How many notebooks were sold? What was Staples revenue for notebooks in 2013?
  2. Sarah goes to Staples and buys 8 notebooks, on sale for 15% off. The notebooks are subject to a 7.5% New Jersey sales tax. The final price of one notebook is 2.98. What was the original price?
  3. Staples also sells pens. Pens ordinarily cost $1.55 each. This month, they are on sale in Vermont for 18% off, but are subject to an 8% sales tax. What is the final price of the pens?
  4. The final price of an item is F. The initial price is P. If the item is on sale for 22% off but subject to a 19% tax, find the value of P in terms of F.
  5. The quantity of pens supplied can be described as a function of price (p) such that s(p)=80+4p. The quantity of pens demanded can be described as a function of price(p) such that d(p)=100-12p. How do s(p) and d(p) differ?
    1. A market clears when supply equals demand. At what quantity and price does the market clear?
  6.  is directly related to 3r. When m is 4, r is 10. Find r when m is 7.
  7. F(x)=5x-1/2
    1. F(x)=ax+b Interpret a and b.
    2. If F(7m)=80m, find all values of m.
  8. h$=4-10h If 3c$=90c, find all values of c.
  9. x∆c=4x-5xc+10c If 4∆3b=10b, find b∆b.
  10. a∇b=5a-3b+abc If 10∇10=1200, find 5∇6.
  11. n people purchase a gift (g) for $l. m people purchase another gift (p) for $q. If n>m and l<q, find the difference in price between g and p.
  12. F(x)=3-10x If F(2b)=100b, find all values of b.
  13. If F(m-3)=2m+7, find F(10).