For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a . As x → − ∞ , f x → _ _ _ _ _ . b . As x → − 3 − , f x → _ _ _ _ _ . c . As x → − 3 + , f x → _ _ _ _ _ . d . As x → ∞ , f x → _ _ _ _ _ . e . The graph is increasing over the interval s _ _ _ _ _ . f . The graph is decreasing over the interval s _ _ _ _ _ . g . The domain is _ _ _ _ _ . h . The range is _ _ _ _ _ . i . The vaertical asymptote is the line _ _ _ _ _ . j . The horizontal asymptote is the line _ _ _ _ _ .
For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1) a . As x → − ∞ , f x → _ _ _ _ _ . b . As x → − 3 − , f x → _ _ _ _ _ . c . As x → − 3 + , f x → _ _ _ _ _ . d . As x → ∞ , f x → _ _ _ _ _ . e . The graph is increasing over the interval s _ _ _ _ _ . f . The graph is decreasing over the interval s _ _ _ _ _ . g . The domain is _ _ _ _ _ . h . The range is _ _ _ _ _ . i . The vaertical asymptote is the line _ _ _ _ _ . j . The horizontal asymptote is the line _ _ _ _ _ .
Solution Summary: The author explains how to fill the blanks in the statement with the help of the following graph.
For Exercises 13-16, refer to the graph of the function and complete the statement. (See Example 1)
a
. As
x
→
−
∞
,
f
x
→
_
_
_
_
_
.
b
. As
x
→
−
3
−
,
f
x
→
_
_
_
_
_
.
c
. As
x
→
−
3
+
,
f
x
→
_
_
_
_
_
.
d
. As
x
→
∞
,
f
x
→
_
_
_
_
_
.
e
. The graph is increasing over the interval
s
_
_
_
_
_
.
f
. The graph is decreasing over the interval
s
_
_
_
_
_
.
g
. The domain is
_
_
_
_
_
.
h
. The range is
_
_
_
_
_
.
i
. The vaertical asymptote is the line
_
_
_
_
_
.
j
. The horizontal asymptote is the line
_
_
_
_
_
.
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
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