Lecture Link:
https://sas.elluminate.com/mr.jnlp?suid=M.7CED3CEEC79C4DF3034CCD955B1A8B&sid=2008170
8.2 Functions
Objective: understand function notation
Examples:
1. If
, find
a)
b)
c)
2. If
find
a)
b)
c)
d)
3. A theater’s total profit is given by the function
dollars, of an individual ticket. Determine the value of
, where is the cost, in
and interpret its meaning.
8.4 Slope, Modeling, and Linear Relationships
Homework – Page 516 #7, 11, 13, 53, 55, 57, 59, 61, 67. Submit it by Tuesday morning.
Objectives:
1. Recognize slope as a rate of change.
2. Use the slope-intercept form to construct models from graphs.
3. Use the point-slope form to construct models from graphs.
Notes: Slope =
Examples:
2. The purcasing power of the dollar is measured by comparing the current price of items to the price of
those same items in 1982. From the chart below you will see that the purchasing power of the dollar
has steadily declined for the years 1990 through 2003. This means that $1 buys less each year.
a) Using 1990 as the reference year, determine a linear function that can be used to estimate the
purchasing power, P, for the years 1990 through 2003. In the function, let t represent the
number of years since 1990.
b) Using the function from part a), estimate the purchasing power of the dollar in 1994. Compare
your answer with the graph to see whether the graph supports your answer.
c) Assuming this trend continues, what would be the purchasing power of the dollar in 2006?
d) Assuming this trend continues, when would the purchasing power of the dollar reach $0.426?
4. The number of calories burned for 1 hour on a treadmill going at a constant speed is a function of
the incline of the treadmill. At 4 miles per hour an average person on a incline will burn 525
calories. At 4 mph on a
burned and
incline the average person will burn 880 calories. Let
be the calories
be the degrees of incline of the treadmill.
a) Determine a linear function
that fits the data. Determine the number of calories burned by the
average person in 1 hour on a treadmill going 4 miles per hour and at a
incline.