(a) The following equation can be solved explicitly for N(t) using the technique of partial fractions. r>0 Solve for N(t). (Enter your answer in terms of t, r. K, and N(0). Use N, for N(0).) N(t) = Note that appropriate values for r. K, and N(0) are r= 1, K = 1, and N(0) = 0.01 (fish per cubic meter of seawater, say). The graph of N(E) is called a sigmoid growth curve. Plot N(t) as a function of t for 0sts 10 N N 1.0- 1.0 1.0 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 2 6. 8 10 4 8 10 2 4 6. 8 10
(a) The following equation can be solved explicitly for N(t) using the technique of partial fractions. r>0 Solve for N(t). (Enter your answer in terms of t, r. K, and N(0). Use N, for N(0).) N(t) = Note that appropriate values for r. K, and N(0) are r= 1, K = 1, and N(0) = 0.01 (fish per cubic meter of seawater, say). The graph of N(E) is called a sigmoid growth curve. Plot N(t) as a function of t for 0sts 10 N N 1.0- 1.0 1.0 0.8 0.8 0.8 0.6 0.6 0.6 0.4 0.4 0.4 0.2 0.2 0.2 2 6. 8 10 4 8 10 2 4 6. 8 10
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter5: Systems Of Equations And Inequalities
Section5.3: Partial Fractions
Problem 7E
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Transcribed Image Text:(a) The following equation can be solved explicitly for N(t) using the technique of partial fractions.
r> 0
dt
Solve for N(t). (Enter your answer in terms of t, r, K, and N(0). Use No for N(0).)
N(t) =
Note that appropriate values for r, K, and N(0) are r= 1, K = 1, and N(0) = 0.01 (fish per cubic meter of seawater, say). The graph of N(t) is called a sigmoid growth curve. Plot N(t) as a function of t for 0 sts 10.
N
N
1.0
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
2
4
6.
8
10
4
6.
10
2
4
6.
10
N
0.8
0.6
Transcribed Image Text:0.8
0.6
0.4
0.2
2
4.
6.
8
10
(b) The value of r can tell us a lot about the ecology of a species-sardines, where females mature in less than one year and have millions of eggs, have a high r, while sharks, where females bear a few live young each year, have a low
r. Play with r and explain how it affects the shape of the curve. (Select all that apply.)
O increasing the value of r means that the population asymptotes to K quicker
D increasing the value of r means that the population asymptotes to K slower
U decreasing the value of r means that the population asymptotes to K quicker
O decreasing the value of r means that the population asymptotes to K slower
O changing the value of r has no affect on when the population asymptotes to K
If a marine protected area is put in place to stop overfishing, which species, sardines or sharks, will recover quickest?
O sardines
O sharks
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