and (F) and Explain in practical terms what your answer means. (Round your answers to one decimal place.) This means that a sole which is__ years old is about __inches long.
and (F) and Explain in practical terms what your answer means. (Round your answers to one decimal place.) This means that a sole which is__ years old is about __inches long.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
(E) and (F) and
Explain in practical terms what your answer means. (Round your answers to one decimal place.)
This means that a sole which is__ years old is about __inches long.
Transcribed Image Text:For this exercise, round all regression parameters to three decimal places.
In the fishery sciences, it is important to determine the length of a fish as a function of its age. One common approach, the von Bertalanffy model, uses a decreasing exponential function of age to
describe the growth in length yet to be attained; in other words, the difference between the maximum length and the current length is supposed to decay exponentially with age. The following table
shows the length L, in inches, at age t, in years, of the North Sea sole.
t= ageL= length t= age L = length
1
3.7
5
12.7
2
3
7.5
13.5
10.0
14.0
11.5
The maximum length attained by the sole is 14.8 inches.
14.4
(a) Make a table showing, for each age, the difference D between the maximum length and the actual length L of the sole.
t = age
D = difference
1
11.1
2
7.3
4.8
3.3
2.1
1.3
3
5
7
0.8
0.4
(b) Find the exponential function that approximates D.
D = 0.303 x 1.585
O D = 2.067 x 1.167
O D = 7.847 x 0.828
D = 19.113 x 0.631
O D = 14.400 x 0.946
(c) Find a formula expressing the length L of a sole as a function of its age t.
O L= 14.8 – 0.303 x 1.585
O L= 14.8 - 2.067 x 1.167
O L= 14.8 - 7.847 x 0.828
L = 14.8 - 19.113 x 0.631
O L= 14.8 - 14.400 x 0.946
Transcribed Image Text:(d) Draw a graph of L versus t.
L.
L.
15
15
10
1아
8
10
12
14
8
10
12
14
15
15
10
10
t
12
14
8.
10
12
14
10
(e) If a sole is 13 inches long, how old is it? (Use the model found in part (c). Round your answer to one decimal place.)
yr
(F) Calculate L(10). (Use the model found in part (c). Round your answer to three decimal places.)
Explain in practical terms what your answer means. (Round your answers to one decimal place.)
This means that a sole which is
years old is about
inches long-
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