Concept explainers
a.
To find: a curve to model the data and superimpose it on a
a.
Answer to Problem 37E
Explanation of Solution
Given information: Population Growth Table shows the population of Laredo, Taxes for selected years between 1950 and 2003.
Years after 1950 | Population |
0 | 10,571 |
20 | 81,437 |
30 | 138,857 |
40 | 180,650 |
50 | 215,794 |
53 | 218,027 |
Calculation:
Using logistic regression utility, a curve the model of the above table data is:
The graph of the above model using graphing utility is shown below.
b.
To find: what number will the Laredo population approach in the long run based on the regression equation.
b.
Answer to Problem 37E
233620.
Explanation of Solution
Given information:
Calculation:
c.
To find: when would the Laredo population first exceed 225,000 people based on the regression equation.
c.
Answer to Problem 37E
In 2006, the Laredo population first exceeds 225,000 people based on the regression equation.
Explanation of Solution
Given information:
Calculation:
Therefore, in 1990 +59 = 2006, the Laredo population first exceeds 225,000 people based on the regression equation.
d.
To write: a logistic differential equation in the form
d.
Answer to Problem 37E
Explanation of Solution
Given information:
Calculation:
Using the long-term carrying capacity from part (b) and the growth rate from the logistic regression in part (a), plug those into the logistic differential equation to find:
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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