Exercise 6.3

19. Landscaping Grading equipment used for landscaping cost $300 plus $60 per hour or part of an hour thereafter.

a. Write an expression for the cost of a cost of a job lasting n hours.

b. If the answer to part (a) is the nth terms of a sequence, write the first 6 terms of this sequence.

23.Interest If $1000 is invested at 5% interest compounded annually, write a sequence that gives the amount in the end of each of the first 4 years.

29. Bouncing Ball A ball is dropped from 128 feet. It rebound1/4 of the height from which it falls every time it hit the ground. How high will it bounce after it hits the ground for the fourth time?

31. Profit If changing market conditions cause a company earning a profit of $8,000,000 this year to project decreases of 2% of its profit in each of the next 5 years, what profit does it project does it project 5 years from now?

37. Rabbit Breeding The number of pairs of rabbits in the population during the first 6 month can be written in the Fibonacci sequence

1,1,2,3,5,8….,

39. Credit Card Debt Kirsten has a $10,000 credit card debt. Each month she pays 1% interest plus a payment of 10% of monthly balance. If she makes no new purchases, write a sequence that gives the payment for the first 4 months.

Exercise 6.4

21. Profit A new firm loses $2000 in its first month, but its profit increase by $400 in each succeeding month for the rest of the year. What is its profit for the first years?

23. Bee Ancestry A female bee hatches from a fertilized egg whereas a male bee hatches from an unfertilized egg. Thus, a female bee has a male parent and a female parent wheras a male bee has only a female parent. Therefore, the numbers of ancestors a male bee follow the Fibonacci sequence

1, 2, 3, 5, 8, 13…..

Use this sequence to determine the total number of ancestors of a male bee back four generations.

25. Clocks A grandfather clock strikes a chime indicating each hour of the day, so that it chimes 3 times at 3:00, 10 times at 10:00, and so on.

a. How many times will It chime in a 12 hour period?

b. How many times will it chime in a 24- hour’s day?

29. Pumps A pumps removes 1/3 of the water in a container with every stroke. After 4 strokes, what amount of water is still in a container that originally had 81 cm³ of water?

33. Credit Card Debt Kirsten has a $10,000 credit card debt. She makes a minimum payment of 10% of the balance at the end of each month. If she makes no new purchases, how much does she owe at the end of 1 year?

35. Bouncing Ball A ball is dropped from 128 feet. It rebounds ¼ of the height from which it falls every time it hits the ground. How far will it have traveled up and down when it hits the ground for the fifth time?

39. Annuities Find the 8-year future value of an annuity with a contribution of $100 at the end of each month into an account that pays 12% per year compounded monthly.

Group Activity

In the 1970s, a local teachers’ organization in Pennsylvania asked for $1000 raise at the end of each year for the next 3 years. When the school board said it could not afford to do this, the teachers’ organization then said that the teachers would accept a $300 raise at the end of each 6 month period. The school board initially responded favorably because the members thought it would save them $400 per year teacher.

If you are an employee, would you rather be given a raise of $1000 at the end of each year (Plan I) or be given a $300 raise at the end of each 6-month period (Plan II)? To answer the question, complete the table for an employee whose base salary is $40,000 (or $20,000 for each 6-month period), and then answer the questions below.

Year / Period (In months) / Plan I / Number Ordered
1 / 0-6
6-12 / 20,000
20,000 / 20,000
20,300
2 / 12-18
18-24 / 20,500
20,500 / 20,600
20,900
3 / 24-30
30-36
Total for 3 Years

Question: If there were 200 teachers in the school district, how much extra would Plan II cost over Plan I for the 4 years?