Math 141-copyright Joe Kahlig, 11B
Page 1
Section 1.3 and 1.4: Linear Functions and Modeling
Points: (3, 4), (7, 16)
Slope:
y2 − y1
x2 − x1
Equation of a line:
Example: The percent of people with an iPad was at 6% at the beginning of 2010 and is projected to
grow linearly so that at the beginning of 2014 the percent of people with an iPad is projected to be 26%.
A) Derive an equation of the line that represents this information.
B) Using this equation, find the percent of people with an iPad at the beginning of 2012.
C) In what year will the percentage of homes with digital TV service be 49%?
Math 141-copyright Joe Kahlig, 11B
Page 2
Example: A minicomputer purchased at a cost of $60,000 in 1988 has a scrap value of $12,000 at the
end of four years. If the value of the computer depreciates linearly,
A) Find a linear equation that represents the minicomputer’s value at the end of t years.
B) Find the minicomputer’s value at the end of the third year.
C) What is the rate of depreciation of the computer?
Example: The Monde Company makes a wine cooler with a capacity of 24 bottles. Each wine cooler
sells for $245. The monthly fixed cost incurred by the company are $381,300, and the variable cost of
producing each wine cooler is $90.
A) Find the Cost, Revenue, and Profit functions.
B) How many coolers should be made and sold when the company breaks even?
C) What is the break even point?
Math 141-copyright Joe Kahlig, 11B
Page 3
Example: Advertising revenue for a local newspaper was $500,000 in 1990 when the population of the
city was 60,000. The paper estimates that advertising revenue rises $2500 for each population increase
of 1000 in their city.
A) Find a linear function that will give advertising revenue as a function of the population of the city.
B) If the population increases by 3500 from its 1990 figure, what will be the expected advertising
revenue?
Example: Paul manages a t-shirt store which has a monthly rent of $805. If Paul needs to sell 46
shirts each month to break even and he sells the shirts for $28.50, what does Paul pay for each shirt?
Supply and Demand functions:
The supply function is a formula that relates the number of items being supplied by manufacturers,
x, to the price of the items, p.
The demand function is a formula that relates the number of items being demanded by consumers,
x, to the price of the items, p.
Note: All points for supply and demand formulas are given as (x, p).
Market equilibrium is the point where the supply and demand functions intersect.
Math 141-copyright Joe Kahlig, 11B
Page 4
Example: When a coffee maker is priced at $40, 200 sell. If the price increases by $10, then 150 sell.
The producer is willing to provide 240 coffee makers when the price is $160 and are willing to provide
120 coffee makers when the price is $88. Find the supply and demand equations and then find the
equilibrium point.
Example: The supplier of Purple Widgets will not market any if the price per item is $2.50 or less. If
the price is $3.50 per box, they will make 400 boxes available per week.
A) Find the supply function.
B) The weekly demand function for Purple Widgets is given by x+200p = 800. What is the equilibrium
quantity?