math 110: exam 4 review. jeopardy captain’s log log on !and the log goes to...... the exponential...
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![Page 1: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/1.jpg)
MATH 110: Exam 4 Review
![Page 2: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/2.jpg)
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
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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
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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
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Captain’s Log 100
• Combine into a single logarithm
• Answer:
yx aaa log2loglog
y
xa
2log
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Captain’s Log 200
• Combine into a single logarithm:
• Answer:
zyx aaa 2loglog31log
zy
xa 32
1log
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Captain’s Log 300
• Expand the logarithm completely:
• Answer:
3
1
2
2
ln
e
yx
2lnln23
1 yx
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Captain’s Log 400
• Expand completely:
• Answer:
25
10log
ab
ba 555 log2log10log
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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
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Log On! 200
• Solve for t:
• Answer:
04.003.0 te
03.0
04.0ln
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Log On! 300
• Solve for x:
• Answer:
5.01
205.0
xe
05.0
3ln
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Log On! 400
• Use natural logs to solve:
• Answer:
379 45 xx
5ln94ln7
4ln3
![Page 13: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/13.jpg)
And the log goes to . . . 100
• Solve:
• Answer:
12log12log xx
8
21
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And the log goes to . . . 200
• Solve:
• Answer: -1
2log3log 22 xx
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And the log goes to . . . 300
• Solve:
• Answer: 2
yyy log2log6log
![Page 16: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/16.jpg)
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
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. . . 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
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. . . 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
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. . . 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
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. . . 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
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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
![Page 22: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/22.jpg)
It all adds up for 400
• Find the sum:
• Answer: 2.999998
13
1
1
3
12
i
i
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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
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It all adds up 800
• Find the sum of the infinite geometric series:
• Answer: 0.2609
001536.00192.024.0
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“Its all Greek to me!” 200
• Find the sum:
• Answer: 58
5
2
2 1k
k
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“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
![Page 27: MATH 110: Exam 4 Review. Jeopardy Captain’s Log Log On !And the Log goes to...... The exponential function 100 200 300 400](https://reader030.vdocuments.net/reader030/viewer/2022032800/56649d435503460f94a1eb48/html5/thumbnails/27.jpg)
“It’s all Greek to me!” 600
• Compute the sum:
• Answer: 2825
15
1
2 132k
kk
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“Its all Greek to me!” 800
• Find
• Answer: -1155
35
1
23n
n
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Number Patterns 200
• Find the closed formula for the nth term of the sequence 4, 7, 10, 13, 16
• Answer: 13 nan
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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
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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
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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