Question

3.) (4 pts) Sunlight from the surface becomes weaker the deeper you are in water. Lu- minous flux, ?, is a measure of the perceived power of light. The SI unit of luminous flux is the lumen (lm). You have measured the luminous flux at various depths (d, in meters) in a lake. When you plot the data as shown in the figure below, the data seem to follow a straight line with a slope of -0.274 and an intercept of 2.71. log(?) 2.5 1.5 2 1 1 2 3 4 5 6 d (a) Based on this data, which of the following equations should you propose as a model for ?(d)? In all cases, a and b are undetermined constants. • ? = $ae^{bd}$ • ? = ad + b • ? = $ad^b$ • ? = $a \log(d) + b$ (b) For various reasons, all of the above models (except the one you hopefully chose!) are actually unphysical; you could have ruled them out without even seeing the data. Pick one you didn't choose and briefly explain why it's unphysical. Hint: consider what each model predicts for luminous flux at the surface of the lake, and also the behavior of ? as d increases toward ?. 2 (c) Based on the information provided, what are the best fit values of the parameters a and b? Include the appropriate units! (d) Use your fit formula to answer this question: at what depth does the luminous flux drop to only 10% of the value at the lake's surface?

          3.) (4 pts) Sunlight from the surface becomes weaker the deeper you are in water. Lu-
minous flux, ?, is a measure of the perceived power of light. The SI unit of luminous
flux is the lumen (lm). You have measured the luminous flux at various depths (d, in
meters) in a lake. When you plot the data as shown in the figure below, the data seem
to follow a straight line with a slope of -0.274 and an intercept of 2.71.
log(?)
2.5
1.5
2
1
1
2
3
4
5
6
d
(a) Based on this data, which of the following equations should you propose as a
model for ?(d)? In all cases, a and b are undetermined constants.
• ? = $ae^{bd}$
• ? = ad + b
• ? = $ad^b$
• ? = $a \log(d) + b$
(b) For various reasons, all of the above models (except the one you hopefully chose!)
are actually unphysical; you could have ruled them out without even seeing the
data. Pick one you didn't choose and briefly explain why it's unphysical. Hint:
consider what each model predicts for luminous flux at the surface of the lake,
and also the behavior of ? as d increases toward ?.
2
(c) Based on the information provided, what are the best fit values of the parameters
a and b? Include the appropriate units!
(d) Use your fit formula to answer this question: at what depth does the luminous
flux drop to only 10% of the value at the lake's surface?

3.) (4 pts) Sunlight from the surface becomes weaker the deeper you are in water. Lu-
minous flux, ?, is a measure of the perceived power of light. The SI unit of luminous
flux is the lumen (lm). You have measured the luminous flux at various depths (d, in
meters) in a lake. When you plot the data as shown in the figure below, the data seem
to follow a straight line with a slope of -0.274 and an intercept of 2.71.
log(?)
2.5
1.5
2
1
1
2
3
4
5
6
d
(a) Based on this data, which of the following equations should you propose as a
model for ?(d)? In all cases, a and b are undetermined constants.
• ? = ae^bd
• ? = ad + b
• ? = ad^b
• ? = a log(d) + b
(b) For various reasons, all of the above models (except the one you hopefully chose!)
are actually unphysical; you could have ruled them out without even seeing the
data. Pick one you didn't choose and briefly explain why it's unphysical. Hint:
consider what each model predicts for luminous flux at the surface of the lake,
and also the behavior of ? as d increases toward ?.
2
(c) Based on the information provided, what are the best fit values of the parameters
a and b? Include the appropriate units!
(d) Use your fit formula to answer this question: at what depth does the luminous
flux drop to only 10% of the value at the lake's surface?

Added by Sophia M.

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