Kwiki H02
1. Let P t represent the number of wolves in a population
at time t years, when t ≥ 0 . The population P t is
increasing at a rate directly proportional to 800 − P t ,
where the constant of proportionality is k.
Kwiki H02
1. Let P t represent the number of wolves in a population
at time t years, when t ≥ 0 . The population P t is
increasing at a rate directly proportional to 800 − P t ,
where the constant of proportionality is k.
a. Write a differential equation that represents the
information described above.
a. Write a differential equation that represents the
information described above.
b. Separate the variables and find P t in terms
of t and k. Use as an initial value P 0 = 500 .
b. Separate the variables and find P t in terms
of t and k. Use as an initial value P 0 = 500 .
c. If P 2 = 700 . find k.
c. If P 2 = 700 . find k.
d. Find
lim
t ∞
P t .
d. Find
lim
t ∞
P t .
e. Is this a logistic model for population growth? Why
or why not?
e. Is this a logistic model for population growth? Why
or why not?
_________________________________________________
Calculus
_________________________________________________
Calculus
__________________________________________________
______
Calculus