A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7 % per year. Assuming that this growth rate continues, the model P ( t ) = 327 ( 1.007 ) t − 2018 represents the population P (in millions of people) in year t . According to this model, when will the population of the United States be 415 million people? According to this model, when will the population of the United States be 470 million people?
A Population Model The resident population of the United States in 2018 was 327 million people and was growing at a rate of 0.7 % per year. Assuming that this growth rate continues, the model P ( t ) = 327 ( 1.007 ) t − 2018 represents the population P (in millions of people) in year t . According to this model, when will the population of the United States be 415 million people? According to this model, when will the population of the United States be 470 million people?
Solution Summary: The author explains that the population of the United States in 2018 was 327 million people and was growing at a rate of 0.7% per year.
A Population Model The resident population of the United States in
2018
was
327
million people and was growing at a rate of
0.7
%
per year. Assuming that this growth rate continues, the model
P
(
t
)
=
327
(
1.007
)
t
−
2018
represents the population
P
(in millions of people) in year
t
.
According to this model, when will the population of the United States be
415
million people?
According to this model, when will the population of the United States be
470
million people?
1. Consider the following system of equations:
x13x2 + 4x3 - 5x4 = 7
-2x13x2 + x3 - 6x4 = 7
x16x213x3 - 21x4 = 28
a) Solve the system. Write your solution in parametric and vector form.
b) What is a geometric description of the solution.
7
c) Is v =
7 in the span of the set S=
[28.
1
HE
3
-5
3
·6
? If it is, write v
6
as a linear combination of the vectors in S. Justify.
d) How many solutions are there to the associated homogeneous system for
the system above? Justify.
e) Let A be the coefficient matrix from the system above. Find the set of all
solutions to Ax = 0.
f) Is there a solution to Ax=b for all b in R³? Justify.
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