Perform the inverse transformation to express light intensity as an exponential function of depth in the lake. Display a scatterplot of the original data with exponential model superimposed. Is your exponential function a satisfactory model for the data?

Rui Baldwin 2020-11-16 Answered
Perform the inverse transformation to express light intensity as an exponential function of depth in the lake.
Display a scatterplot of the original data with exponential model superimposed. Is your exponential function a satisfactory model for the data?
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Expert Answer

yagombyeR
Answered 2020-11-17 Author has 92 answers

Step 1
Equation found in exercise 5d (where y^ is the natural logarithm of the light intensity):
[y^=6.78910.330x]
Take the exponential of both sides:
[y^=e6.78910.330x=e6.7891e0.330x]
Step 2
The Depth is on the vertical axis and the light intensity is on the horizontal axis.
image
Step 3
The model is an satisfactory model, because it seems to pass through every single data point.
Result:
Yes.

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