The population of Canada in 2010 was approximately 34 million with an annual growth rate of 0.804 % . At this rate, the population P t (in millions) can be approximated by P t = 34 1.00804 t , where t is the time in years since 2010. a. Is the graph of P an increasing or decreasing exponential function? b. Evaluate P 0 and interpret its meaning in the context of this problem. c. Evaluate P 5 and interpret its meaning in the context of this problem Round the population value to the nearest million. d. Evaluate P 15 and P 25 .
The population of Canada in 2010 was approximately 34 million with an annual growth rate of 0.804 % . At this rate, the population P t (in millions) can be approximated by P t = 34 1.00804 t , where t is the time in years since 2010. a. Is the graph of P an increasing or decreasing exponential function? b. Evaluate P 0 and interpret its meaning in the context of this problem. c. Evaluate P 5 and interpret its meaning in the context of this problem Round the population value to the nearest million. d. Evaluate P 15 and P 25 .
Solution Summary: The author analyzes whether the graph of the function for the population of Canada is an increasing or decreasing exponential function.
The population of Canada in 2010 was approximately 34 million with an annual growth rate of
0.804
%
. At this rate, the population
P
t
(in millions) can be approximated by
P
t
=
34
1.00804
t
,
where t is the time in years since 2010.
a. Is the graph of P an increasing or decreasing exponential function?
b. Evaluate
P
0
and interpret its meaning in the context of this problem.
c. Evaluate
P
5
and interpret its meaning in the context of this problem Round the population value to the nearest million.
2. We want to find the inverse of f(x) = (x+3)²
a. On the graph at right, sketch f(x).
(Hint: use what you know about
transformations!) (2 points)
b. What domain should we choose to
get only the part of f (x) that is one-
to-one and non-decreasing? Give
your answer in inequality notation. (2
points)
-
c. Now use algebra to find f¯¹ (x). (2
points)
-4-
3-
2
1
-4
-3
-2
-1
0
1
-1-
-2-
--3-
-4
-N-
2
3
4
1. Suppose f(x) =
2
4
==
x+3
and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all
x
your work, write neatly so your work is easy to follow, and connect your expressions
with equals signs. (4 points)
College Algebra with Modeling & Visualization (5th Edition)
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