Questions:
1.) The national cost "C" in billions of dollars for dental services can be modeled by the linear equation:
C = 2.85n+ 30.52
where n is the number of years since 1990 (Health Care Financing Administration, www.hcfa.gov).
a) Find and interpret the C-intercept for the line.
b) Find and interpret the n-intercept for the line.
c) Graph the line for n ranging from 0 through 20.
2.) Demand equation. Helen's Health Foods usually sells 400 cans of ProPac Muscle Punch per week when the price is $5 per can. After experimenting with prices for some time, Helen has determined that the weekly demand can be found by using the equation:
d=600-40p
where d is the number of cans and p is the price per can.
a) Will Helen sell more or less Muscle Punch if she raises her price from $5?
b) What happens to her sales every time she raises her price by $1?
c) Graph the equation.
3.) Marginal revenue. A defense attorney charges her client $4000 plus $120 per hour.
The formula R=120n+4000 gives her revenue in dollars for n hours of work.
a) What is her revenue for 100 hours of work?
b) What is her revenue for 101 hours of work?
c) By how much did the one extra hour of work increase the revenue? (The increase in revenue is called the marginal revenue for the 101st hour.)
4.) Gas laws. The volume of a gas is inversely proportional to the pressure on the gas. If the volume is 6 cubic centimeters when the pressure on the gas is 8 kilograms per square centimeter, then what is the volume when the pressure is 12 kilograms per square centimeter?
5.) Graph the linear inequality:
2x<3y+6
6.) Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent.
a) y=-3x+19
y=2x-1
b) y=-4x-7
y=3x
7) Solve each system by Addition Method
a) 3x+5y=-11
x-2y=11
b) 2x=2-4
3x+y=-1
8) Solve each system by the Addition Method. Determine whether the equations are independent, dependent or inconsistent.
a) x-y=3
-6x+6y=17
9) Solve each system by Addition Method
a) 3/7x+5/9y=27
1/9x+2/7y=7
b) 3x-2.5y=7.125
2.5x-3y=7.3125