
Concept explainers
(a)
Tofind:The equation of line for the Manatee population.
(a)

Answer to Problem 37PPS
The equation of the line for the manatee population is
Explanation of Solution
Given:
The manatee’s population inhabited in the Florida’s waters in 1991 = 1267
The rate of increasing the manatee population every year = 123.
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
Considering the population of manatee increases every year with the population of 1991 remaining constant. The population of year 1991 is the intercept of the line on the y- axis while the increasing rate of the population is the slope of the equation.
The total populationP for t yearssince 1991 can be calculated from the equation.
The equation of the straight line in the slope and intercept form is
Therefore, the equation of the straight line is
(b)
Toplot:The graph for the equation of total population of manatee.
(b)

Answer to Problem 37PPS
The plot is drawn below.
Explanation of Solution
Given:
The manatee’s population inhabited in the Florida’s waters in 1991 = 1267
The rate of increasing the manatee population every year = 123.
Calculation:
The standard form of slope and intercept form of the straight line is
Here m is the slope of the straight line and c is the y- intercept of the equation.
The equation of the straight line in the slope and intercept form is
Plot this equation on the Cartesian plane.
(c)
Tofind:The total manatee population in 2006.
(c)

Answer to Problem 37PPS
The total population of manatee in the year 2006 is 2251.
Explanation of Solution
Given:
The manatee’s population inhabited in the Florida’s waters in 1991 = 1267
The rate of increasing the manatee population every year = 123.
Calculation:
The equation of the straight line in the slope and intercept form is
From the year 1991 to 2006, there are 15 years. Substitute 15 for t in the equation of total population.
Therefore, the total population of manatee in the year 2006 is 2251.
Chapter 4 Solutions
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