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