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?

Question
Exponential growth and decay
asked 2020-11-16
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?

Answers (1)

2020-11-17
Step 1
Equation found in exercise 5d (where \(\displaystyle\hat{{{y}}}\) is the natural logarithm of the light intensity):
\(\displaystyle{\left[\hat{{{y}}}={6.7891}-{0.330}{x}\right]}\)
Take the exponential of both sides:
\(\displaystyle{\left[\hat{{{y}}}={e}^{{{6.7891}-{0.330}{x}}}={e}^{{{6.7891}}}{e}^{{-{0.330}{x}}}\right]}\)
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.
0

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