As light passes through water, its intensity decreases exponentially with the depth of the water. The data below shows the light intensity (in lumens) at various depths. Depth (ft) Lumens 3 11.5 6 8.6 9 6.7 12 5.2 15 3.8 18 2.9 Let y represent the number of lumens at a depth of a feet. • Linearize this data and create a table of the semi-log data, i.e. the (x, ln(y)) data OR the (x, log(y)) data (your choice). . Find the linear regression equation for the semi-log data. • Use your semi-log equation to find an exponential model for y. Use your exponential model to predict the light intensity (number of lumens) at depth of 29 ft.
As light passes through water, its intensity decreases exponentially with the depth of the water. The data below shows the light intensity (in lumens) at various depths. Depth (ft) Lumens 3 11.5 6 8.6 9 6.7 12 5.2 15 3.8 18 2.9 Let y represent the number of lumens at a depth of a feet. • Linearize this data and create a table of the semi-log data, i.e. the (x, ln(y)) data OR the (x, log(y)) data (your choice). . Find the linear regression equation for the semi-log data. • Use your semi-log equation to find an exponential model for y. Use your exponential model to predict the light intensity (number of lumens) at depth of 29 ft.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 1
As light passes through water, its intensity decreases exponentially with the depth of the water. The data below shows the
light intensity (in lumens) at various depths.
Depth (ft)
Lumens
3
11.5
6
8.6
9
6.7
12
5.2
15
3.8
18
2.9
Let y represent the number of lumens at a depth of x feet.
• Linearize this data and create a table of the semi-log data, i.e. the (x, ln(y)) data OR the (x, log(y)) data (your
choice).
• Find the linear regression equation for the semi-log data.
• Use your semi-log equation to find an exponential model for y.
• Use your exponential model to predict the light intensity (number of lumens) at depth of 29 ft.
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