Answers (Lesson 3-4)

Chapter 3

Answers (Lesson 3-4)

A10

NAME

3-4 Practice

DATE

PERIOD

Exponential and Logarithmic Equations

Solve each equation.

1. 5x = 125x-2 3

2. log6 x + log6 9 = log6 54 6

( ) 3. -19 x + 3 = 27x - -65

5. logx 64 = 3 4

4. e2x - ex - 6 = 0 1.099 6. ln -1e = x -1

7. ln (2x - 1) = ln 16 -127 9. ln (x - 5) + ln 4 = ln x - ln 2 -470

8. 3e4x - 9e2x - 15 = 0 0.7167 10. 4x + 2 = 6-2x - 3 -1.639

11. 6e6x - 17e3x + 7 = 0

0.28 and -0.23

13. 4e2x - 13ex + 9 = 0

0 and 0.811 15. 2-4x + 1 = 32x - 3 0.80

12. 6 ln (x + 2) - 3 = 21 52.6

14. log (2x + 1) + log (x - 4) = log (2x2 - 4)

no solution 16. log5 (x + 4) + log5 x = log5 12 2

17. log (x + 1) + log (x - 3) = log (6x2 - 6) 18. ln 0.04x = -8 0.008 no solution

Solve each equation. Round to the nearest hundredth.

19. 29x = 1210 1.14

20. 43x = 1056 1.67

21. 5x + 3 - 4 = 19 -1.05

22. 3x - 8 + 2 = 38 11.26 23. 62x - 1 = 18 1.31

24. 23 + 2x = 130 2.01

25. BANKING Ms. Cubbatz invested a sum of money in a certificate of deposit that earns 8% interest compounded continuously. The formula for calculating interest that is compounded continuously is A = Pert. If Ms. Cubbatz made the investment on January 1, 2005, and the account was worth $12,000 on January 1, 2009, what was the original amount in the account? $8713.79

26. FINANCIAL LITERACY If $500 is deposited in a savings account providing an annual interest rate of 5.6% compounded quarterly, how long will it take for the account to be worth $750? 7.29 years

Chapter 3

22

Glencoe Precalculus

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NAME

DATE

PERIOD

3-4 Word Problem Practice

Exponential and Logarithmic Equations

1. RADIOACTIVE DECAY The amount of radium A present in a sample after t years can be modeled by A = A0e-0.00043t, where A0 is the initial amount. How long will it take 50 grams to decay to 10 grams? 3743 years

2. INTERNET The table shows the number of hits an Internet blog received for three weeks.

5. RADIOACTIVITY The amount of radioactivity in a sample is given by the equation ln (N) - ln (N0 ) = -kt, where N is the current level, N0 is the original level, k is the decay rate, and t is the time elapsed in hours. If the decay rate is 0.070, how many grams would be left after 24 hours if the original amount was 1000 grams? 186.4 grams

Week

1 2 3

Number of Hits 1000

1250

1563

a. Write an exponential model to find the number of hits N in week w.

N = 1000(1.25)w - 1

b. In what week will the blog get

10,000 hits? 12th week

6. BIOLOGY A certain strain of bacteria in a perfect growth medium doubles in population every 8 hours.

a. If there were 100 bacteria at t = 0 hours, complete the table below.

Time (hr) 8 16 24 32 40

Number of doubles

1

2

3

4

5

Population 200 400 80016003200

3. RICHTER SCALE The function used to measure the magnitude R of an earthquake is given by R = 0.67 log (0.37E) + 1.46, where E is the energy in kilowatt hours that is released by the earthquake. If the magnitude of an earthquake is 6.0, find the approximate energy released.

about 17,288,942 kilowatt hr

4. INTEREST RATE The effective annual yield E for an account that is compounded n times per year at r percent is given by the formula E = 1 + -nr n - 1. Suppose an account pays 5%. Use a calculator to find how many compounding periods it would take for the effective yield to be 5.1%.

5

b. Write an equation to model the

number of bacteria N at time t given

NN0,=thNe 0i(n2it)ia-8t ,l

number

or N =

of bacteria.

100(2)-8t

c. Suppose a chemical is added that kills exactly one half of the bacteria at the 16-hour mark. Write an equation to find the number of bacteria after the 16-hour mark.

N = 200(2)- t -8 2

d. Using the formula in part c, find how long it will take for the number of

bacteria to reach 5000. 39.2 hr

Chapter 3

23

Glencoe Precalculus

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 3-4

Glencoe Precalculus

005_032_PCCRMC03_893804.indd 22

10/1/09 1:55:55 PM 005_032_PCCRMC03_893804.indd 23

10/1/09 1:56:46 PM

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download