Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P = e − k x , where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Refer to Exercise 75, and find the euphotic depth for Lake Tahoe and for Lake Erie. Round to the nearest tenth of a meter.
Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by P = e − k x , where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76. Refer to Exercise 75, and find the euphotic depth for Lake Tahoe and for Lake Erie. Round to the nearest tenth of a meter.
Solution Summary: The author calculates the depth at which the light intensity falls to 1% of the value from the surface for Lake Tahoe and Lake Erie.
Sunlight is absorbed in water, and as a result the light intensity in oceans, lakes, and ponds decreases exponentially with depth. The percentage of visible light, P (in decimal form). at a depth of x meters is given by
P
=
e
−
k
x
,
where k Is a constant related to the clarity and other physical properties of the water. The graph shows models for the open ocean. Lake Tahoe, and Lake Erie for data taken under similar conditions. Use these models for Exercises 73-76.
Refer to Exercise 75, and find the euphotic depth for Lake Tahoe and for Lake Erie. Round to the nearest tenth of a meter.
an you tell how old a lobster is by its size? This question was investigated by the authors of a paper that appeared in the Biological Bulletin (August 2007). Researchers measured carapace (the exterior shell) length of 27 laboratory-raised lobsters of known age. The data on x = carapace length (in mm) and y = age (in years) in the following table were read from a graph that appeared in the paper.
Age
CarapaceLength
Age
CarapaceLength
Age
CarapaceLength
1.00
63.32
1.82
118.25
2.93
147.82
1.00
67.50
2.18
108.24
2.92
140.17
1.00
69.58
2.18
109.64
2.92
135.73
1.00
74.41
2.17
117.99
2.92
121.81
1.42
80.32
2.17
123.81
3.17
141.30
1.42
81.80
2.33
138.47
3.41
151.73
1.42
84.59
2.50
133.95
3.42
145.78
1.82
105.07
2.51
124.25
3.75
147.21
1.82
106.16
2.50
123.51
4.08
152.04
(a)
Construct a scatterplot of these data, and then find the equation of the least squares regression line that describes the relationship between y = age and x = carapace length.
A scatterplot…
(c)
Th
Data Table
Total Length (cm)
138.0
135.0
130.0
120.5
149.0
141.0
141.0
150.0
166.0
151.5
129.5
150.0
Print
Weight (kg)
110
60
90
60
85
105
95
85
155
140
105
110
Done
0
X
Critical Values for the Correlation Coefficient
3 0.997
4
0.950
5
0.878
6
0.811
7
0.754
8
0.707
9 0.666
10 0.632
11 0.602
12 0.576
13 0.553
14 0.532
15 0.514
16 0.497
17 0.482
18 0.468
19 0.456
20 0.444
21 0.433
22 0.423
23 0.413
24 0.404
25 0.396
26 0.388
27 0.381
0371
X
not practical to v
parts (a) through
Some pedometers have a default setting that assumes that the number of steps a person must take to walk 1 mile decreases by 33 steps per 1 inch increase in height. Suppose a person 72 inches tall makes 2,250 steps per mile. Find a linear model of the number of steps S per mile as a function of height h (in inches).
College Algebra with Modeling & Visualization (5th Edition)
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