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Shedding Light on the Subject: Function Models of Light Decay
Part I: Make a Conjecture
Have you ever noticed how the amount of light differs the further you are under water? The amount of light is an important factor in the kinds of plants and animals that exist at a given depth. Examine the underwater images and movies given below.

How does the light intensity change as you go deeper in the ocean?

Two friendly, but one slightly shy, dolphins pose for a picture.

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Think About This Situation

Based on the picture and the movie above, answer the following questions involving light intensity.
  1. How does the light change as the depth increases? Sketch a possible graph of the (depth, light intensity) relationship that you described.
      
  2. What accounts for the change in the light intensity?
     
  3. Suppose you are 10 feet under water, what environmental factors determine the light intensity at 10 feet? If you descend to 15 feet, what determines the light intensity at 15 feet? At 20 feet? Which of these factors remained constant and which changed?
     
  4. If I(d) is the light intensity at a depth d, what does the quantity I(11) – I(10) represent?
     
  5. How would the quantity I(12) – I(11) compare to I(11) – I(10)? What accounts for the difference?

Click here to go to the next step of Gathering Data to verify your conjectures.

 

 

 
Make a Conjecture
Gather Data
Analyze the Data
Reflect on your work

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CD Version last updated: September 21, 2000