The population P t of a herd of deer on an island can be modeled by P t = 1200 1 + 2 e − 0.12 t , where t represents the number of years since the park service has been tracking the herd. a. Evaluate P 0 and interpret its meaning in the context of this problem. b. Use the function to predict the deer population after 4 yr. Round to the nearest whole unit. c. Use the function to predict the deer population after 8 yr. d. Determine the number of years required for the deer population to reach 900. Round to the nearest year. e. What value will the term 2 e 0.12 t approach as t → ∞ ? f. Determine the limiting value of P t .
The population P t of a herd of deer on an island can be modeled by P t = 1200 1 + 2 e − 0.12 t , where t represents the number of years since the park service has been tracking the herd. a. Evaluate P 0 and interpret its meaning in the context of this problem. b. Use the function to predict the deer population after 4 yr. Round to the nearest whole unit. c. Use the function to predict the deer population after 8 yr. d. Determine the number of years required for the deer population to reach 900. Round to the nearest year. e. What value will the term 2 e 0.12 t approach as t → ∞ ? f. Determine the limiting value of P t .
Solution Summary: The author calculates the population of a herd of deer at P(t), where t represents the time in years.
The population
P
t
of a herd of deer on an island can be modeled by
P
t
=
1200
1
+
2
e
−
0.12
t
,
where
t
represents the number of years since the park service has been tracking the herd.
a. Evaluate
P
0
and interpret its meaning in the context of this problem.
b. Use the function to predict the deer population after 4 yr. Round to the nearest whole unit.
c. Use the function to predict the deer population after 8 yr.
d. Determine the number of years required for the deer population to reach 900. Round to the nearest year.
e. What value will the term
2
e
0.12
t
approach as
t
→
∞
?
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