2.1 Linear Functions and Equations
Modeling with linear functions:
f(t) = (constant rate of change) t + (initial amount)
slope
intercept
In 1945, the average salary in the USA was approximately $24,000 (2006 inflation adjusted dollars). By 1975, the average salary in the USA increased to $45,000 (2006 inflation adjusted dollars). Assuming a linear increase in salaries during that period, find a model for the average salary (2006 inflation adjusted dollars) in the USA t years after 1945:
1
Consider this fuel consumption data for a 2000 Honda Civic:
Gallons of Gasonline
10
11
5
Miles Travelled
345
374
167.5
Find a linear model for miles traveled (y) as a function of gallons of gas (x):
Use the average of the 3 slopes (miles per gallon). The y-intecept is obviously ______ .
2
Piecewise defined functions.
Example:
3
A rental car company has a car rental deal based on miles driven: It costs $75 dollars to rent the car for the week and for each mile beyond 100 miles driven, you are charged $1 a mile.
Construct a piecewise linear model for the cost (C) of driving x miles:
if 0 ≤ x ≤ 100
C(x) =
if x > 100
4
You try:
A car is travelling at 30 mph, and then it begins to slow down at a constant rate of 6 mph every 4 seconds. Find a linear model f
(t) for the speed of the car t seconds after it starts to slow.
5