171S1.3 Linear functions, slope, applications
August 19, 2010
MAT 171 Dr. Claude Moore, CFCC
Section 1.3 Linear Functions, Slope, and Applications
Session 1 introduces the Course, CourseCompass, and Chapter 1: Graphs, Functions, and Models.
This session is available in CourseCompass. Read the Announcements to find Session 1.
If the CFCC website is not available, you may access the following with links:
• Campus Cruiser : http://prod.campuscruiser.com/cfcc/
• WebAdvisor: http://reg.cfcc.edu
I suggest that you view the examples that were not worked in your section. If you have questions or need assistance, please contact me or go to the Math Lab (S606) or the Learning Lab (L Building).
Dr. Moore
Aug 19­7:45 AM
Aug 19­8:31 AM
Section 1.3 Linear Functions, Slope, and Applications
In Exercises 1 4, the table of data contains input output values for a function. Answer the following questions for each table. a) Is the change in the inputs x the same? b) Is the change in the outputs y the same? c) Is the function linear?
110/2.
110/4.
Aug 19­8:39 AM
Aug 19­7:45 AM
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171S1.3 Linear functions, slope, applications
Section 1.3 Linear Functions, Slope, and Applications
Find the slope of the line containing the given points.
110/6.
August 19, 2010
Section 1.3 Linear Functions, Slope, and Applications
Find the slope of the line containing the given points.
111/16.
110/8.
111/20.
Aug 19­7:45 AM
Section 1.3 Linear Functions, Slope, and Applications
Find the slope of the line containing the given points.
111/26.
Aug 19­7:45 AM
Section 1.3 Linear Functions, Slope, and Applications
Determine the slope, if it exists, of the graph of the given linear equation.
111/32.
111/28.
111/38.
Aug 19­7:45 AM
Aug 19­7:45 AM
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171S1.3 Linear functions, slope, applications
August 19, 2010
Section 1.3 Linear Functions, Slope, and Applications
Section 1.3 Linear Functions, Slope, and Applications
111/40. HIV Cases. HIV, human immunodeficiency virus, spreads to 10 people 112/44. Credit­ Card Debt. From 1992 to 2006, the average household credit­ card every minute. It is estimated that there were about 40.3 million cases of HIV worldwide in 2005. The estimated number of cases in 1985 was about 2 million. ( Source: UNAIDS) Find the average rate of change in the number of adults and children worldwide with HIV from 1985 to 2005.
Aug 19­7:45 AM
Section 1.3 Linear Functions, Slope, and Applications
112/50. Find the slope and the y­ intercept of the line with the given equation: y = 4 / 7.
balance has risen 172%. Use the data in the graph below to find the average rate of change in the average credit­ card balance from 1992 to 2006.
Aug 18­8:10 PM
Section 1.3 Linear Functions, Slope, and Applications
112/60. Find the slope and the y­intercept of the line with the given equation: f(x) = 0.3 + x
112/54. Find the slope and the y­ intercept of the line with the given equation: 2x ­ 3y = 12.
Aug 19­7:45 AM
Aug 19­7:45 AM
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171S1.3 Linear functions, slope, applications
August 19, 2010
Section 1.3 Linear Functions, Slope, and Applications
Section 1.3 Linear Functions, Slope, and Applications
113/66. Graph equation using the slope and the y­intercept: 2x + 3y = 15
113/70. Pressure at Sea Depth. The function P, given by P = (1/33)d + 1, gives the pressure, in atmospheres (atm), at a depth d, in feet, under the sea. a) Graph P. b) Find P(0), P(5), P(10), P(33), and P(100).
Answers from TI calculator: P(0) = 1, P(5) = 1.1515, P(10) = 1.303, P(33) = 2, and P(100) = 4,1818
Aug 19­7:45 AM
Section 1.3 Linear Functions, Slope, and Applications
113/71. Stopping Distance on Glare Ice. The stopping distance (at some fixed speed) of regular tires on glare ice is a function of the air temperature F, in degrees Fahrenheit. This function is estimated by D(F) = 2F + 115, where is the stopping distance, in feet, when the air temperature is F, in degrees Fahrenheit. a) Graph D. b) Find D(0), D(­20), D(10), and D(32). c) Explain why the domain should be restricted to [­57.5, 32].
Answers from TI calculator:
D(0) = 115, D(­20) = 75, D(10) = 135, and D(32) = 179
Since D(­57.5) = 0 represents a stopping distance of zero, the smallest value for F is ­57.5. If the temperature is above 32 degrees F, the ice turns to water. Thus, the domain is [­57.5, 32].
Aug 19­7:45 AM
Aug 19­7:45 AM
Section 1.3 Linear Functions, Slope, and Applications
113/74. Straight­Line Depreciation. A marketing firm buys a new color printer for $ 5200 to print banners for a sales campaign. The printer is purchased on January 1 and is expected to last 8 yr, at the end of which time its trade­in, or salvage, value will be $ 1100. If the company figures the decline or depreciation in value to be the same each year, then the salvage value V, after t years, is given by the linear function V(t) = 5200 ­ 512.50t, for 0 < t < 8. a) Graph V. b) Find V(0), V(1), V(2), V(3), and V(8). c) Find the domain and the range of this function.
(b) V(0) = 5200, V(1) = 4687.5, V(2) = 4175, V(3) = 3662.5, and V(8) = 1100
(c) Domain is [0, 8] and range is [1100, 5200]. Why?
Aug 19­7:45 AM
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