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Answer the following questions dealing with Regression Analysis.
Grab your graphing calculator.
| 1. |
Which of the following graphs would
have a negative linear correlation closest to
negative one?
Choose:
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| 2. |
The table shows the amount of medicine for treating a
disease in the bloodstream over the 9 hours following a dose of 10
mg. It seems that the rate of decrease of the drug is
approximately proportional to the amount remaining.
a.) Use this information to find a suitable function
to model this data.
b.) Using your model, when will there be less than
1 mg. of the medicine in the patient's bloodstream?
c.) If the initial does was 15 mg., when would the
amount of the medicine in the bloodstream fall below 5 mg?
Express answers in this question rounded to
three decimal places.
|
Time
(hrs) |
Drug
Amount
(mg) |
| 0 |
10 |
| 1 |
8.3 |
| 2 |
7.2 |
| 3 |
6.0 |
| 4 |
5.0 |
| 5 |
4.4 |
| 6 |
3.7 |
| 7 |
2.8 |
| 8 |
2.5 |
Answer |
|
| 3. |
A factory is
producing and stockpiling metal sheets to be shipped
to an automobile manufacturing plant. The
factory ships only when there is a minimum of 2,050
sheets in stock at the beginning of that day. The table shows the day,
x,
and the number of sheets in stock, f (x),
at the beginning of that day.
a.) Write a linear regression
equation for this set of data, rounding coefficients
to four decimal places.
b.) Use this equation to
determine the day the sheets will be shipped. |
| Day |
Sheets
in Stock |
| 1 |
860 |
| 2 |
930 |
| 3 |
1000 |
| 4 |
1150 |
| 5 |
1200 |
| 6 |
1360 |
Answer |
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| 4. |
Since January
1980, the population of the city of Brownville has grown
according to the mathematical model
 ,
where x is the number of years since January
1980.
a.) Explain what the
numbers 720,500 and 1.022 represent in this model.
b.) If this trend
continues, use this model to predict the year during
which the population of Brownville will reach 1,548,800. |
Answer |
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| 5. |
According to the National Weather Service, the 2005 average
monthly temperature in degrees Fahrenheit at Central Park in New
York City is given below:
|
Month |
Jan. |
Feb. |
March |
April |
May |
June |
July |
Aug. |
Sept. |
Oct. |
Nov. |
Dec. |
Average
Temp (º F) |
31.3 |
36.5 |
39.4 |
55.1 |
58.9 |
74.0 |
77.5 |
79.7 |
73.3 |
57.9 |
49.6 |
35.3 |
a.) Write a sinusoidal function that models the average monthly
temperature, using t = 1 to represent January. Round
values to three decimal places. b.) According to your model, what is the average temperature in
December? c.) Explain the discrepancy from your model to the
average monthly temperature in December?
Answer |
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6. |
At the local
arcade, the most popular video game is Cosmic Blaster.
Joshua decides to observe new game players using the machine every
half hour and record their highest scores.
a.) Find an equation to model the data.
b.) According to your model, what score
would most likely be observed at 8:15 pm?
Answer to the nearest integer.
c.) Joshua makes the assumption
that the more expert players use the machine later in
the evening. Does the data support this hypothesis?
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Answer |
|
Time |
Score |
|
4 pm |
950 |
|
4:30 pm |
1001 |
|
5 pm |
1450 |
|
5:30 pm |
1503 |
|
6 pm |
1605 |
|
6:30 pm |
3002 |
|
7 pm |
2668 |
|
7:30 pm |
2860 |
|
8 pm |
3250 |
|
8:30 pm |
3945 |
|
9 pm |
4720 |
|
9:30 pm |
4866 |
|
10 pm |
5509 |
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