Suppose that a population follows a logistic growth pattern, with a limiting population N . If the initial population is denoted by P 0 , and t is the amount of time elapsed, then the population P can be represented by P = P 0 N P 0 + N − P 0 e − k t . where k is a constant related to the growth rate. a. Solve for t (note that there are numerous equivalent algebraic forms for the result). b. Interpret the meaning of the resulting relationship.
Suppose that a population follows a logistic growth pattern, with a limiting population N . If the initial population is denoted by P 0 , and t is the amount of time elapsed, then the population P can be represented by P = P 0 N P 0 + N − P 0 e − k t . where k is a constant related to the growth rate. a. Solve for t (note that there are numerous equivalent algebraic forms for the result). b. Interpret the meaning of the resulting relationship.
Solution Summary: The author calculates t from the expression P=1kmathrmlncdot.
Suppose that a population follows a logistic growth pattern, with a limiting population N. If the initial population is denoted by
P
0
,
and
t
is the amount of time elapsed, then the population P can be represented by
P
=
P
0
N
P
0
+
N
−
P
0
e
−
k
t
.
where k is a constant related to the growth rate.
a. Solve for t (note that there are numerous equivalent algebraic forms for the result).
b. Interpret the meaning of the resulting relationship.
1. Given the vector field F(x, y, z) = -zi, verify the relation
1
VF(0,0,0) lim
+0+ volume inside S
ff F• Nds
S.
where S, is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
Let a = (-4, 5, 4) and 6 = (1,0, -1).
Find the angle between the vector
1) The exact angle is cos
2) The approximation in radians is
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