MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential...

MATH 110: Exam 4 Review

Jeopardy

Captain’s Log

Log On ! And the Log goes to . . .

. . . The exponential function

100 100 100 100

200 200 200 200

300 300 300 300

400 400 400 400

Double Jeopardy

It all adds up Its all Greek to me!

Number Patterns

200 200 200

400 400 400

600 600 600

800 800 800

Final Jeopardy

• When a murder is committed, the body, originally 37 0C, 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 0C and the surrounding air temperature is a constant 22 0C.

• A body is found at 4 pm with a temperature of 30 0C. Determine the time of death. Express your answer as an actual time, i.e. 8:26 pm.

• Answer: 7:13 am

kteTtH 15

Captain’s Log 100

• Combine into a single logarithm

• Answer:

yx aaa log2loglog

y

xa

2log

Captain’s Log 200

• Combine into a single logarithm:

• Answer:

zyx aaa 2loglog31log

zy

xa 32

1log

Captain’s Log 300

• Expand the logarithm completely:

• Answer:

3

1

2

2

ln

e

yx

2lnln23

1 yx

Captain’s Log 400

• Expand completely:

• Answer:

25

10log

ab

ba 555 log2log10log

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:

04.003.0 te

03.0

04.0ln

Log On! 300

• Solve for x:

• Answer:

5.01

205.0

xe

05.0

3ln

Log On! 400

• Use natural logs to solve:

• Answer:

379 45 xx

5ln94ln7

4ln3

And the log goes to . . . 100

• Solve:

• Answer:

12log12log xx

8

21

And the log goes to . . . 200

• Solve:

• Answer: -1

2log3log 22 xx

And the log goes to . . . 300

• Solve:

• Answer: 2

yyy log2log6log

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

1log676 3 ttS

. . . 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

teA 0035.056

. . . 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

kteP 000,225

. . . 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

rtCeA

. . . 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

ktePP 0

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: 2.999998

13

1

1

3

12

i

i

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

32 09.160009.160009.1600600

It all adds up 800

• Find the sum of the infinite geometric series:

• Answer: 0.2609

001536.00192.024.0

“Its all Greek to me!” 200

• Find the sum:

• Answer: 58

5

2

2 1k

k

“Its all Greek to me!” 400

• Write the following sum using sigma notation:

• Answer:

21

100

9

16

7

9

5

4

3

1

10

1

2

12k k

k

“It’s all Greek to me!” 600

• Compute the sum:

• Answer: 2825

15

1

2 132k

kk

“Its all Greek to me!” 800

• Find

• Answer: -1155

35

1

23n

n

Number Patterns 200

• Find the closed formula for the nth term of the sequence 4, 7, 10, 13, 16

• Answer: 13 nan

Number Patterns 400

• Which of the following represent an arithmetic sequence (choose all that apply):5, 8, 11, 14, 17, . . .

• Answer: all except the 2nd and 3rd

na

na

na

n

n

n

21

12

1

,4,3,2,12

2222

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

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

,5.337,225,150,100

,64

1,

36

1,

16

1,4

1

,26

1,

17

1,

10

1,5

1,2

1

1

12 n 22

1

n 15.1100 n