Textbook Chapter 1

26 Chapter 1 Prerequisites for Calculus
Quick Review 1.3 (For help, go to Section 1.3.)
In Exercises 1–3, evaluate the expression. Round your answers to
3 decimal places.
1. 5 23 2.924 2. 3 2 4.729
3. 3 1.5 0.192
In Exercises 4–6, solve the equation. Round your answers to
4 decimal places.
4. x 3 17 2.5713 5. x 5 24 1.8882
6. x 10 1.4567 1.0383
In Exercises 7 and 8, find the value of investing P dollars for n years
with the interest rate r compounded annually.
7. P $500, r 4.75%, n 5 years $630.58
8. P $1000, r 6.3%, n 3 years $1201.16
)
)
In Exercises 9 and 10, simplify the exponential expression.
9. x
3y2
2
x
4y3
3 x 18 y 5 1
b2
2
c2
1
x
1 8 10.
y ( 5 a3 c4
( a4 b3
a 2 b 1 c 6 a2
b c6
Section 1.3 Exercises
1. Domain: All reals Range: (, 3) 2. Domain: All reals Range: (3, )
In Exercises 1–4, graph the function. State its domain and range.
1. y 2 x 3 2. y e x 3
3. y 3 • e x 2 4. y 2 x 1
Domain: All reals Range: (2, ) Domain: All reals Range: (, 1)
In Exercises 5–8, rewrite the exponential expression to have the indicated
base.
5. 9 2x , base 3 3 4x 6. 16 3x , base 2 2 12x
7. (18) 2x , base 2 2 6x 8. (127) x , base 3 3 3x
In Exercises 9–12, use a graph to find the zeros of the function.
9. f (x) 2 x 5 2.322 10. f (x) e x 4 1.386
11. f (x) 3 x 0.5 0.631 12. f (x) 3 2 x 1.585
In Exercises 13–18, match the function with its graph. Try to do it
without using your grapher.
13. y 2 x (a) 14. y 3 x (d) 15. y 3 x (e)
16. y 0.5 x (c) 17. y 2 x 2 (b) 18. y 1.5 x 2 (f)
(a)
(c)
(e)
(b)
(d)
(f)
19. Population of Nevada Table 1.9 gives the population of
Nevada for several years.
Table 1.9
Population of Nevada
Year Population (thousands)
1998 1,853
1999 1,935
2000 1,998
2001 2,095
2002 2,167
2003 2,241
Source: Statistical Abstract of the United States,
2004–2005.
(a) Compute the ratios of the population in one year by the population
in the previous year. 1.0443, 1.0326, 1.0485, 1.0344, 1.0341
(b) Based on part (a), create an exponential model for the population
of Nevada. One possibility is 1853(1.04) n
(c) Use your model in part (b) to predict the population of
Nevada in 2010. 2,967 thousand, or 2,967,000
20. Population of Virginia Table 1.10 gives the population of
Virginia for several years.
Table 1.10 Population of Virginia
Year Population (thousands)
1998 6,901
1999 7,000
2000 7,078
2001 7,193
2002 7,288
2003 7,386
Source: Statistical Abstract of the United States,
2004–2005.
(a) Compute the ratios of the population in one year by the
population in the previous year. 1.0143, 1.0111, 1.0162, 1.0132, 1.0134
(b) Based on part (a), create an exponential model for the
population of Virginia. One possibility is 6901(1.013) n
(c) Use your model in part (b) to predict the population of
Virginia in 2008. 7,852 thousand, or 7,852,000