MATH 110: Exam 4 Review

Jeopardy Captain’s Log Log On !And the Log goes to The exponential function

Double Jeopardy It all adds upIts all Greek to me! Number Patterns

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

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

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

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

Captain’s Log 400 Expand completely: Answer:

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

Log On! 200 Solve for t: Answer:

Log On! 300 Solve for x: Answer:

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

And the log goes to Solve: Answer:

And the log goes to Solve: Answer: -1

And the log goes to Solve: Answer: 2

And the log goes to 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: months

... 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

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

... 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: hours

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

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

It all adds up for 400 Find the sum: Answer:

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,

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

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

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

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

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

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

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

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

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