Concept explainers
To calculate the populations of Colorado C and Minnesota M from the year 2013 to 2020 modeled by the equations:
Answer to Problem 89E
From the years 2017 to 2020, the population in Colorado C is greater than the population in Minnesota M and the estimated point of intersection is
Explanation of Solution
Given information: The population models of Colorado C and Minnesota M from the year 2008 to 2012 is given as:
Where,
Calculation:
(a) Using the table feature in the utility to find the population of ColoradoC and Minnesota M from the year 2012 to 2020 is given in the following table:
Year | |||
2008 | 8 | 4895 | 5252 |
2009 | 9 | 4969 | 5285 |
2010 | 10 | 5043 | 5318 |
2011 | 11 | 5117 | 5351 |
2012 | 12 | 5191 | 5384 |
2013 | 13 | 5265 | 5417 |
2014 | 14 | 5339 | 5450 |
2015 | 15 | 5413 | 5483 |
2016 | 16 | 5487 | 5516 |
2017 | 17 | 5561 | 5549 |
2018 | 18 | 5635 | 5582 |
2019 | 19 | 5709 | 5615 |
2020 | 20 | 5783 | 5648 |
(b) From the above table, it is concluded that in the years 2017, 2018, 2019 and 2020, the population in ColoradoC is greater than the population in Minnesota M
(c)Using the graphical utility to sketch the graph of the following functions:
Enter the expressions
The graph is :
The estimated point of intersection is:
From the above graph it is concluded that the estimated point of intersection is t = 16.71=~17
(d) The algebraic solution of the given equation:
To find the point of intersection, consider that
(e) From the part(b), part(c) and part(d), it is concluded that the years from 2017 to 2020, the population in Colorado C is greater than the population in Minnesota M and the solution of the given equations are the point of intersection, which is approximately
Chapter 7 Solutions
Precalculus with Limits: A Graphing Approach
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