Demographics. The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median household income in the United States grew from about $ 30 , 000 in 1990 to about $ 53 , 000 in 2010. (A) If I represents the median household income and t represents the number of years since 1990, write a linear equation that expresses I in terms of t . (B) Use this equation to estimate median household income in the year 2030.
Demographics. The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median household income in the United States grew from about $ 30 , 000 in 1990 to about $ 53 , 000 in 2010. (A) If I represents the median household income and t represents the number of years since 1990, write a linear equation that expresses I in terms of t . (B) Use this equation to estimate median household income in the year 2030.
Solution Summary: The author calculates the linear equation for I in terms of t using the slope-intercept formula.
Demographics. The median household income divides the households into two groups: the half whose income is less than or equal to the median, and the half whose income is greater than the median. The median household income in the United States grew from about
$
30
,
000
in 1990 to about
$
53
,
000
in 2010.
(A) If
I
represents the median household income and
t
represents the number of years since 1990, write a linear equation that expresses
I
in terms of
t
.
(B) Use this equation to estimate median household income in the year 2030.
EXAMPLE 3
Find
S
X
√√2-2x2
dx.
SOLUTION Let u = 2 - 2x². Then du =
Χ
dx =
2- 2x²
=
信
du
dx, so x dx =
du and
u-1/2 du
(2√u) + C
+ C (in terms of x).
Let g(z) =
z-i
z+i'
(a) Evaluate g(i) and g(1).
(b) Evaluate the limits
lim g(z), and lim g(z).
2-12
(c) Find the image of the real axis under g.
(d) Find the image of the upper half plane {z: Iz > 0} under the function g.
k
(i) Evaluate
k=7
k=0
[Hint: geometric series + De Moivre]
(ii) Find an upper bound for the expression
1
+2x+2
where z lies on the circle || z|| = R with R > 10. [Hint: Use Cauchy-Schwarz]
Chapter 1 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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