grade 11 graphing

[needshelp]

given the information:

The opening paragraph explains how a person suffers from SAD (seasonal affective disorder), and is depressed in the winter because there isn't enough light. She needs to use light therapy during the winter. One hour of light therapy replaces one hour of natural light. She will use light therapy in fall/winter of 03/04 (Sept.21,2003 to March 21,2004)

1. Determine the min amount of light that she would need to be happy.

-my answer is 12 hours because that is the min amount that she can get without light therapy (see circled number on diagram). I think I am right with that.

2. Write an equation for the periodic curve of your graph.

-this is what I am extremely confused on how to do. I think it is a sine or a cosine graph, but I have no clue how to make the equation.

3. Create a model to show how much light therapy she needs from Sept.21,2003 to March 21, 2004 to reach her min total hours of light.

-Does anyone know what they mean by "Create a model"? Is that another equation?

4. Use your model to determine how long she should apply light therapy on Jan 15, 2004, and Feb. 6,2004.
- I might be okay with this question if I knew what the model to use was.

Thanks in advance for any help you may be able to give.

 

[stapel]

1) Since the point of the therapy is to avoid being sad, I'm not sure how you're getting that the no-therapy amount is the minimum she needs, since then she wouldn't need the therapy...? Also, how are you getting that "twelve hours" is the minimum day length? The table shows something quite different...?

Eliz.

 

[needshelp]

1) Since the point of the therapy is to avoid being sad, I'm not sure how you're getting that the no-therapy amount is the minimum she needs, since then she wouldn't need the therapy...? Also, how are you getting that "twelve hours" is the minimum day length? The table shows something quite different...?

Eliz.

its light therapy, and the minium is the minium amount of light she needs a day to be happy. This can be just normal day light or if needed, light therapy. So when its not sept.21-march.21, she has enough natural light, so she doesnt need light therapy.
the "12 hours" is what i think is the minium amount of light (natural or therapy) she needs a day. I am assuming this because I crossed out any days between sept 21 and march 21, and 12 was the lowest amount of daylight on a day where she didn't need the light therapy (theres enough natural light).

 

[soroban]

Hello, needshelp!

I can help with #2 . . .

given the information:

| Date  | Day |  Hrs |
+-------+-----+------+
| 12-31 |   0 |  9.1 |
| 01-30 |  30 |  9.9 |
| 02-28 |  60 | 11.2 |
| 03-31 |  90 | 12.7 |
| 04-30 | 120 | 14.0 |
| 05-30 | 150 | 15.0 |
| 06-29 | 180 | 15.3 |
| 07-29 | 210 | 14.6 |
| 08-28 | 240 | 13.3 |
| 09-27 | 270 | 11.9 | \
| 10-27 | 300 | 10.8 |  |
| 11-26 | 330 |  9.6 |  |
| 12-26 | 360 |  9.1 |  | Light therapy period
| 01-25 | 390 |  9.6 |  |
| 02-24 | 420 | 11.0 |  |
| 03-26 | 450 | 12.0 | /
+-------+-----+------+

1. Determine the min amount of light that she would need to be happy.
I don't understand the question.
\(\displaystyle \;\;\)They should define her "happy level" <u>exactly</u>.
Is she "happy" during the rest of the year (April through August),
\(\displaystyle \;\;\;\)when she gets at least 13.3 hours of daylight?
[I don't think 12 is the minimum . . . just my opinion.]

2. Write an equation for the periodic curve of your graph.

Assuming the graph is sinusoidal, it has a period of 360 days.
\(\displaystyle \;\;\)On day 0, it has a low of 9.1
\(\displaystyle \;\;\)On day 180, it has a high of 15.3
\(\displaystyle \;\;\)On day 360, it returns to the low of 9.1

          |
     15.3 +          ***
          |        *  :  *
          |      *    :    *
     12.2 + - - * - - : - - * - - - - -
          |    *      :      *
          |  *        :        *     *
      9.1 **          :          ***
          |           :           :
        --+-----------+-----------+---
          0          180         360

It is an inverted cosine function: \(\displaystyle \:y\:=\:-\cos\theta\)

The angle \(\displaystyle \theta\) is a fraction of \(\displaystyle 2\pi\).
\(\displaystyle \;\;\;\)If \(\displaystyle x\) is the number of days, the fraction is \(\displaystyle \,\frac{x}{360}\)
\(\displaystyle \;\;\;\)Hence: \(\displaystyle \;\theta\,=\,\frac{x}{360}(2\pi}\,=\,\frac{\pi}{180}x\)

So far, we have: \(\displaystyle \:y\:=\:-\cos\left(\frac{\pi}{180}x\right)\)


The axis of the curve is at \(\displaystyle \ y\,=\,12.2\\) (instead of \(\displaystyle y\,=\,0\)).

\(\displaystyle \;\;\;\)The graph is raised 12.2 units: \(\displaystyle \:y\,=\,-\cos\left(\frac{\pi}{180}x\right)\,+\,12.2\)


The amplitude is: \(\displaystyle A\:=\:15.3\,-\,12.2\:=\:3.1\)

\(\displaystyle \;\;\;\)Therefore: \(\displaystyle \L\:y\:=\:-(3.1)\cos\left(\frac{\pi}{180}x\right)\,+\,12.2\)

 

[needshelp]

okay, thats awesome. Thanks.

Do you understand what it means by "Create a model"?