Concept explainers
a.
To find: the years which show greatest increase and greatest decrease using slope of the graph.
a.

Answer to Problem 91E
Greatest increase in profit in years 2011 to 2012.
Greatest decrease in profit is in year 2015 to 2016.
Explanation of Solution
Given:
Following graph is given between net profits (in billions of dollars) and year where 2010 is represented as
Formula used:
Slope of a line is given be
Calculation:
Slopes of each line is calculated in table below.
Thus observing the slopes, it can be said that the years showing greatest increase in profit is 2011 to 2012 and the years showing greatest decrease in profit are 2015 to 2016.
Conclusion:
Slope of the given graph shows the increase or decrease in profit.
A negative slope indicates that the profit has fallen.
b.
To find: An equation for the line between the year 2010 and 2017.
b.

Answer to Problem 91E
Explanation of Solution
Given:
The coordinates of graph for year 2010 are (0, 14.0) and for the year 2017 are (7, 48.4)
Formula used:
Equation of a line in 2 point form is
Calculation:
Slope of the line is
Now, for equation of line
Conclusion:
The line formed between the year 2010 and 2017 is a straight line with the equation
(c)
To interpret: the meaning of slope from point (b).
(c)

Answer to Problem 91E
A positive slope indicating an overall increase in profit over the years.
Explanation of Solution
Given:
The equation of the line is
In an equation of a line a slope means the change in value on y-axis compared to change in value on x-axis.
A positive slope indicates that the value on y-axis is increasing faster as compared to increase in value on x-axis.
In the equation, the slope is 4.91 which means on an average there has been an increase in profit of 4.91 billions of dollars each year.
Conclusion:
A positive slope indicates that there has been an increase in profit each year on an average basis.
d.
To find: estimated net profit in the year 2021 using the equation from part (b) and whether it is accurate.
d.

Answer to Problem 91E
68.01 billions of dollars.
It may be inaccurate.
Explanation of Solution
Given:
The equation of the line is
For the year 2021 x is to be considered as
Calculation:
Conclusion:
On solving the equation, the estimated net profit will be 68.01.
However, one cannot claim the accuracy of this estimate because it is found out using the average increase in profit formula.
The equation used is not an actual equation of the profit, but rather found from the average increase.
One must not forget, that there were many lines in the data given with unequal slope, indicating the unpredictability of the graph.
So, the estimated profit may be correct or incorrect.
Chapter 1 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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