The following table shows the percent increase of donations made on behalf of a non-profit organization for the period of 1984 t
o 2003. Use a
graphing calculator to make a scatter plot of the data. Find an
equation for and graph the line of regression.
Then use the equation to predict the percent donated in the year 2015.
Year
1984
1989
1993
1997
2001
2003
Percent
187.9 213.9 234.7 255.5 276.3 286.7
Year
1984
1989
1993
1997
2001
2003
Percent
187.9 213.9 234.7 255.5 276.3 286.7
1 answer:
In this problem, the dependent variable is the time or the year while the independent variable is the percent increase of donations. We try to plot these data through the years (percent increase vs year) in MS Excel and then obtain the trendline equation. Attached is the graph drawn from the data provided. According to the software, the equation applicable to this data is y = 5.2x - 10129 in which R² = 1. This means the relationship between the two variables is linear and perfect. The slope is positive which means that as the year goes on, the percent increase in donations also increases.
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Answer:
x = 1 or x = ± i
Step-by-step explanation:
Note the sum of the coefficients
1 - 1 + 1 - 1 = 0
This indicates that x = 1 is a root, thus (x - 1) is a factor
Using long division or synthetic division, then
x³ - x² + x - 1 = (x - 1)(x² + 1), thus
(x - 1)(x² + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ± = ± i