Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded 148 N = 1 + 3.6e-2.61t' where t is measured in years and N is measured in thousands of tons of fish.t (a) What is the r value for the Eastern Pacific yellowfin tuna? r = per yr (b) What is the carrying capacity K for the Eastern Pacific yellowfin tuna? K = thousand tons (c) What is the optimum yield level? thousand tons (d) Use your calculator to graph N against t. 200 200

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Chapter2: Second-order Linear Odes
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Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded
148
N =
-2.61t'
1 + 3.6e
where t is measured in years and N is measured in thousands of tons of fish.t
(a) What is the r value for the Eastern Pacific yellowfin tuna?
r =
per yr
(b) What is the carrying capacity K for the Eastern Pacific yellowfin tuna?
K =
thousand tons
(c) What is the optimum yield level?
thousand tons
(d) Use your calculator to graph N against t.
200
200
180
180
160
160
140
140
120
120
N 100
N 100
80
80-
60
60-
40
40
20
20
2
4
6.
10
12
2
6
8
10
12
200
200
180
180
160
160
140
140
120
120
N 100
N 100
80
80
60
60
40
40
20
20
4
6
8
10
12
2
4
6
8
10
12
(e) At what time was the population growing the most rapidly? (Round your answer to two decimal places.)
yr
Transcribed Image Text:Studies to fit a logistic model to the Eastern Pacific yellowfin tuna population have yielded 148 N = -2.61t' 1 + 3.6e where t is measured in years and N is measured in thousands of tons of fish.t (a) What is the r value for the Eastern Pacific yellowfin tuna? r = per yr (b) What is the carrying capacity K for the Eastern Pacific yellowfin tuna? K = thousand tons (c) What is the optimum yield level? thousand tons (d) Use your calculator to graph N against t. 200 200 180 180 160 160 140 140 120 120 N 100 N 100 80 80- 60 60- 40 40 20 20 2 4 6. 10 12 2 6 8 10 12 200 200 180 180 160 160 140 140 120 120 N 100 N 100 80 80 60 60 40 40 20 20 4 6 8 10 12 2 4 6 8 10 12 (e) At what time was the population growing the most rapidly? (Round your answer to two decimal places.) yr
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