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Find the linear function y , where y depends on $\text{\hspace{0.17em}}x,$ the number of years since 1980.
$y=-\text{3}00x+\text{11},\text{5}00$
Find and interpret the y -intercept.
For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500.
Assume the population is changing linearly.
a) 800 b) 100 students per year c) $\text{\hspace{0.17em}}P\left(t\right)=\text{1}00t+\text{17}00$
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.
Find a formula for the moose population, $\text{\hspace{0.17em}}P.$
What does your model predict the moose population to be in 2020?
18,500
For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in [link] . Assume that the house values are changing linearly.
Year | Pima Central | East Valley |
---|---|---|
1970 | 32,000 | 120,250 |
2010 | 85,000 | 150,000 |
In which subdivision have home values increased at a higher rate?
If these trends were to continue, what would be the median home value in Pima Central in 2015?
$91,625
Draw a scatter plot for the data in [link] . Then determine whether the data appears to be linearly related.
0 | 2 | 4 | 6 | 8 | 10 |
–105 | –50 | 1 | 55 | 105 | 160 |
Draw a scatter plot for the data in [link] . 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 |
Extrapolation
Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in [link] . 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 |
For the following exercises, consider the data in [link] , 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 |
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.
Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
$x$ | 17 | 20 | 23 | 26 | 29 |
$y$ | 15 | 25 | 31 | 37 | 40 |
Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
$x$ | 10 | 12 | 15 | 18 | 20 |
$y$ | 36 | 34 | 30 | 28 | 22 |
$y=-1.294x+49.412;r=-0.974$
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:
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