1. MATH 110: Exam 4 Review

2. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400

3. Double Jeopardy It all adds upIts all Greek to me! Number Patterns 200 400 600 800

4. Final Jeopardy When a murder is committed, the body, originally 37 0 C, cools according the function In this function H is the temperature of the body in Celsius t hours after death. T and k are constants with T representing the temperature of the surrounding air. Suppose that after two hours the temperature of the body is 35 0 C and the surrounding air temperature is a constant 22 0 C. A body is found at 4 pm with a temperature of 30 0 C. Determine the time of death. Express your answer as an actual time, i.e. 8:26 pm. Answer: 7:13 am

5. Captain’s Log 100 Combine into a single logarithm Answer:

6. Captain’s Log 200 Combine into a single logarithm: Answer:

7. Captain’s Log 300 Expand the logarithm completely: Answer:

8. Captain’s Log 400 Expand completely: Answer:

9. Log On! 100 How long would it take to double your investment if you invest $2000 at 7.5% compounded quarterly? Answer: around 9.3 years

10. Log On! 200 Solve for t: Answer:

11. Log On! 300 Solve for x: Answer:

12. Log On! 400 Use natural logs to solve: Answer:

13. And the log goes to... 100 Solve: Answer:

14. And the log goes to... 200 Solve: Answer: -1

15. And the log goes to... 300 Solve: Answer: 2

16. And the log goes to... 400 New employees are given an initial exam and then retested monthly with an equivalent exam. The average score for the employees is give by: t is measured in months since the initial exam Approximately when would the average score by 54? Answer: 55.16 months

17. ... The exponential function 100 The concentration of a pollutant in parts per million in the atmosphere increases exponentially by the function t is the number of years after 1960 When will the concentration reach 70 parts per million? Answer: 2023

18. ... The exponential function 200 The population, P, of a city is given by t = 0 is the year 1991. In 1971, the population was 210,000. Find k to predict the population in the year 2000. Answer: 232,095

19. ... The exponential function 300 Suppose 80 ounces of a radioactive substance decays to 9 ounces in three hours. Use the equation to determine how long does it takes for the substance to decay to half its initial value? Answer: 0.951 hours

20. ... The exponential function 400 The median price of a home rose from $50,000 in 1970 to $100,000 in 1990. Assuming exponential growth by the equation when would the median price reach $150,000. Answer: 2001

21. It all adds up 200 This year college tuition is $4,000. Every year after, it will increase by $500 Find the total amount of money it will cost you graduate from college if it takes you 6 years if you begin this year. Answer: $31,500

22. It all adds up for 400 Find the sum: Answer: 2.999998

23. It all adds up 600 A company contributes to each of its employees’ retirement funds by depositing $600 at the end of each year in a retirement account for the employee. The account pays 9% interest compounded annually. How much will an employee’s retirement fund be after working for 20 years? Answer: $30, 696.07

24. It all adds up 800 Find the sum of the infinite geometric series: Answer: 0.2609

25. “Its all Greek to me!” 200 Find the sum: Answer: 58

26. “Its all Greek to me!” 400 Write the following sum using sigma notation: Answer:

27. “It’s all Greek to me!” 600 Compute the sum: Answer: 2825

28. “Its all Greek to me!” 800 Find Answer: -1155

29. Number Patterns 200 Find the closed formula for the nth term of the sequence 4, 7, 10, 13, 16 Answer:

30. Number Patterns 400 Which of the following represent an arithmetic sequence (choose all that apply): 5, 8, 11, 14, 17,... Answer: all except the 2 nd and 3 rd

31. Number Patterns 600 Find the first term of a geometric sequence given that the second term is -6 and the fifth term is 0.75. Answer: 12

32. Number Patterns 800 Find a closed formula for each of the following sequences: Which of these represent a geometric sequence? Answer: ; only the last sequence is geometric