Math MethodsName______

Supplemental Problems

Chapter 7-8

Simplify
1. / 2.
Solve without logs.
3. / 4.
5. / 6.
7. / 8.
9. / 10.
11. Each day as part of a fitness program, Josie is timed over a 400 metre run. Her times for this run are modeled by the function where T is the time she takes for the run and w is the number of weeks after she starts the program.
  1. Find the time Josie takes for the 400 metre run at the start of the program
  2. Find the best time she can expect for the 400 metre run
  3. Find the number of weeks Josie could expect to train before she can complete the run in 65 seconds

Solve for x. Give exact answers.
12. / 13.
14. Simplify / 15. Evaluate correct to four significant figures:
a. b.
16. Given that , find / 17.
18. / 19. Simplify to a single log:
20.
/ 21.
22. / 23.
24. / 25.
26. / 27.
28. Solve the system: and
29. The 8th term of an arithmetic sequence is -1. The 19th term is 21. Find the 142nd. / 30. Given is arithmetic, find x and y.

31. The sixth term of an arithmetic sequence is 5 while the sum of the first 9 terms is 72. Find the sum of the first 24 terms. / 32. An arithmetic series has first term -50 and common difference 4. How many terms must be taken before the sum of the series first exceeds 100?

33. The engineers who are responsible for the condition of a new bridge are trying to calculate the future costs of corrosion protection starting from the year the bridge was built (t=0). There are two stages in corrosion protection: Preparation, which includes the removal of flaking paint and corroded metal. Preparation costs $180 per hour. Painting. This involves the application of paint to the prepared metal. The engineers estimate that by the end of the first year of operation (t=1) they will have had to spend 7 hours in preparation for painting. Because it is anticipated that the bridge will deteriorate, they expect to have to spend 9 hours in preparation during the second year (t=2) with the time increasing by 2 hours per year for each successive year. If is the time spent on preparation in year t, then etc. in arithmetic progression. A complete coat of paint costs $6000 for the first year, but this cost is expected to rise by 7% per year.
  1. Find the time expected to be spent on preparation in the tenth year .

  1. Find a formula for the cost of preparation in terms of t.

  1. Find the total time spent on preparation over the first 20 years of operation of the bridge.

  1. The engineers budget to spend a total of $180,000 on preparation. How long will this money last?

  1. Find a formula for the cost of the paint in the nth year (in terms of n).

34. Find the value of the series: giving answer in the form . / 35. Find the sum of the even numbers that are between 99 and 999.
36. Find x such that forms a geometric sequence. / 37. Consider the series: How many terms of this series must be taken before the sum first exceeds ?

38. A radioactive source decays at the rate of 1% of its activity per day. On the first day, a source registered 5000 disintegrations.
a. How many disintegrations could be expected on the second day?
  1. On which day do the number of disintegrations first fall below 4000?
  2. How many disintegrations in total could be expected to be recorded if this source is observed for 30 days?

39. The third and seventh terms of a geometric sequence are and respectively. Find the 14th term. What term is equal to ? / 40. Find the sum
41. A geometric series has nine terms, a common ratio of 2 and a sum of 3577. Find the first term. / 42 Write as a rational number.
43. To what amount will $1800 grow to if it is invested at 3.5% p.a. for 12 years, compounding every 6 months?

ANSWERS:

MM Supplemetal Problems Ch 7-8.06

1.

2.

3. x= -6

4.

5.

6.

7. use graphs: 2.26

8. use graphs: 1.13

9. x= -1

10. use graphs: -.418

11a. 70 sec

11b. 62.3 sec

11c. 4.29 weeks

12. 13

13.

14.

15a. 1.365

15b. -.6477

16. .045

17.

18.

19.

20. 1,

21. -.415

22. 4 or

23. .264

24. .0187

25. 2.463

26. 1.609 or 0

27. 1.893 or 0

28.

29. 267

30.

31. -348

32. 28

33a. 25

33b.

33c. 520 hrs

33d. 28.7 yrs

33e.

34.

35. 247,050

36. .351 or -2.85

37. 11

38a. 4950

38b. 23 days

38c. 130,150

39.

40. .577

41. 7

42.

43. $2729.60

MM Supplemetal Problems Ch 7-8.06