The population on an island is modeled by P(t)=600040+60e−0.03t P
(
t
)
=
6000
40
+
60
e
−
0.03
t
for t≥0
t
≥
0
, where P(t)
P
(
t
)
is the number of people on the island after t
t
years. What is limt→∞P(t)
lim
t
→
∞
P
(
t
)
?

600040

Step-by-step explanation:

Given the population of people on an island modeled by the equation P(t)=600040+60e−0.03t for t≥0 where P(t) is the number of people on the island after years. To get limt→∞P(t), we will substitute infinity into the equation as shown;

limt→∞ 600040+60e−0.03t

= 600040+60e−0.03(∞)

= 600040+60e−∞

= 600040+60(1/e∞)

Note that 1/e∞ = 1/∞ = 0

Hence the equation becomes;

= 600040+60(0)

=  600040

Hence  limt→∞P(t) is 600040

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