Algebra and Trigonometry 2e1-81

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20. Find the equation of a line
with a y- intercept of
and slope
21. Sketch a graph of the linear
function
22. Find the point of
intersection for the 2 linear
functions:
23. A car rental company
offers two plans for renting
a car.
Plan A: 25 dollars per day
and 10 cents per mile
Plan B: 50 dollars per day
with free unlimited mileage
How many miles would you
need to drive for plan B to
save you money?
Modeling with Linear Functions
24. Find the area of a triangle
bounded by the y axis, the
line and
the line perpendicular to
that passes through the
origin.
25. A town’s population
increases at a constant
rate. In 2010 the
population was 55,000. By
2012 the population had
increased to 76,000. If this
trend continues, predict
the population in 2016.
26. The number of people
afflicted with the common
cold in the winter months
dropped steadily by 50
each year since 2004 until
2010. In 2004, 875 people
were inflicted.
Find the linear function
that models the number of
people afflicted with the
common cold C as a
function of the year,
When will no one be
afflicted?
For the following exercises, use the graph in Figure 1 showing the profit, in thousands of dollars, of a company in a
given year, where represents years since 1980.
Figure 1
27. Find the linear function y, where y depends on
the number of years since 1980.
28. Find and interpret the y-intercept.
4 • Exercises 391
For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had
grown to 2,500.
ⓐ How much did the population grow between
the year 2004 and 2012?
ⓑ What is the average population growth per
year?
ⓒ Find an equation for the population, P, of the
school t years after 2004.
29. Assume the population is changing linearly.
For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By
2010, the population was measured to be 12,500. Assume the population continues to change linearly.
30. Find a formula for the
moose population, .
31. What does your model
predict the moose
population to be in 2020?
For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley
(adjusted for inflation) are shown in Table 1. Assume that the house values are changing linearly.
Year Pima Central East Valley
1970 32,000 120,250
2010 85,000 150,000
Table 1
32. In which subdivision have
home values increased at a
higher rate?
33. If these trends were to
continue, what would be
the median home value in
Pima Central in 2015?
392 4 • Exercises
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Fitting Linear Models to Data
34. Draw a scatter plot for the
data in Table 2. Then
determine whether the
data appears to be linearly
related.
0 -105
2 -50
4 1
6 55
8 105
10 160
Table 2
35. Draw a scatter plot for the
data in Table 3. If we
wanted to know when the
population would reach
15,000, would the answer
involve interpolation or
extrapolation?
Year Population
1990 5,600
1995 5,950
2000 6,300
2005 6,600
2010 6,900
Table 3
36. Eight students were asked
to estimate their score on a
10-point quiz. Their
estimated and actual
scores are given in Table 4.
Plot the points, then sketch
a line that fits the data.
Predicted Actual
6 6
7 7
7 8
8 8
7 9
9 10
10 10
10 9
Table 4
37. Draw a best-fit line for the plotted
data.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city of people 25
years or older who are college graduates is given below, by year.
Year 2000 2002 2005 2007 2010
Percent Graduates 6.5 7.0 7.4 8.2 9.0
Table 5
4 • Exercises 393
38. Determine whether the
trend appears to be linear.
If so, and assuming the
trend continues, find a
linear regression model to
predict the percent of
unemployed in a given
year to three decimal
places.
39. In what year will the
percentage exceed 12%?
40. Based on the set of data given
in Table 6, calculate the
regression line using a
calculator or other technology
tool, and determine the
correlation coefficient to three
decimal places.
17 20 23 26 29
15 25 31 37 40
Table 6
41. Based on the set of data given
in Table 7, calculate the
regression line using a
calculator or other technology
tool, and determine the
correlation coefficient to three
decimal places.
10 12 15 18 20
36 34 30 28 22
Table 7
For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The
following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded
years:
42. Use linear regression to
determine a function
where the year depends on
the population, to three
decimal places of accuracy.
43. Predict when the
population will hit 12,000.
44. What is the correlation
coefficient for this model to
three decimal places of
accuracy?
45. According to the model,
what is the population in
2014?
Practice Test
1. Determine whether the
following algebraic equation
can be written as a linear
function.
2. Determine whether the
following function is
increasing or decreasing.
3. Determine whether the
following function is
increasing or decreasing.
394 4 • Exercises
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4. Find a linear equation that
passes through (5, 1) and (3,
–9), if possible.
5. Find a linear equation, that
has an x intercept at (–4, 0)
and a y-intercept at (0, –6), if
possible.
6. Find the slope of the line in Figure
1.
Figure 1
7. Write an equation for line in Figure 2.
Figure 2
8. Does Table 1 represent a linear function? If so, find
a linear equation that models the data.
–6 0 2 4
14 32 38 44
Table 1
9. Does Table 2 represent a linear function? If so, find
a linear equation that models the data.
x 1 3 7 11
g(x) 4 9 19 12
Table 2
10. At 6 am, an online
company has sold 120
items that day. If the
company sells an average
of 30 items per hour for
the remainder of the day,
write an expression to
represent the number of
items that were sold after
6 am.
4 • Exercises 395