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
Question

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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.
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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