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.
5
Use the method of disks to find the volume of the solid that is obtained
when the region under the curve y = over the interval [4,17] is rotated
about the x-axis.
3. Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
4. Use cylindrical shells to find the volume of the solid generated when the
region enclosed by the given curves is revolved about the x-axis.
y = √√x, y = 0, y = √√3
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