3.The asymptote of the graph of
A.is the x-axis B. is the y-axis
C.has equation D. has equation.
4.In your own words, describe the characteristics of the graph of an exponential function.
Use the exponential function defined by (Exercise 5)and the words asymptote,
domain,and rangein your explanation.
Graph each exponential function. See Examples 1–3.
8. 9. 10.
11. 12.
13.Concept Check For an exponential function defined by , if , the
graph from left to right. If , the graph from
(rises/falls) (rises/falls)
left to right.
14.Concept Check Based on your answers in Exercise 13,make a conjecture (an educated
guess) concerning whether an exponential function defined by is one-to-one.
Then decide whether it has an inverse based on the concepts of Section 10.1.
Solve each equation. See Examples 4 and 5.
21. 22. 23.
24. 25. 26.
Use the exponential key of a calculator to find an approximation to the nearest thousandth.
A major scientific periodical published an
article in 1990 dealing with the problem of
global warming. The article was accompa-
nied by a graph that illustrated two possi-
ble scenarios.
(a)The warming might be modeled by an
exponential function of the form
(b)The warming might be modeled by a
linear function of the form
In both cases, x represents the year, and y represents the increase in degrees Celsius due
to the warming. Use these functions to approximate the increase in temperature for each of the
following years.
- 2000 34. 2010 35. 2020 36. 2040
y=0.009x-17.67.
y= 1 1.046* 10 -^3821 1.0444x 2.
0.64.917 2.7182.5 2.718-3.1
12 2.6 13 1.8 0.53.921
a
4
3
b
x
=
27
64
a
3
2
b
x
=
8
27
10 x=0.1
3 x= 5 x=0.2
1
81
5 x=
1
125
8 x= 4 162 x+^1 = 64 x+^392 x-^8 = 27 x-^4
6 x= 36 8 x= 64 100 x= 1000
ƒ 1 x 2 =ax
06 a 61
ƒ 1 x 2 =ax a 71
y= 22 x-^2 y= 22 x+^1
g 1 x 2 = a y= 4 - x y= 6 - x
1
5
b
x
g 1 x 2 = a
1
3
b
x
ƒ 1 x 2 = 3 x ƒ 1 x 2 = 5 x
ƒ 1 x 2 = 3 x
x= 1 y= 1
ƒ 1 x 2 =ax
586 CHAPTER 10 Inverse, Exponential, and Logarithmic Functions
