SOLUTION: A logistic growth model for a certain small state is given by P(t)= 240/5+54.99e^0.0208t, where t is the number of years since 1997 and P(t) is in millions. Find the following:

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Question 41572: A logistic growth model for a certain small state is given by
P(t)= 240/5+54.99e^0.0208t, where t is the number of years since 1997 and P(t) is in millions. Find the following:
a) Find the population in the year 2006.
b) In what year will the population reach 24 million?
c) What happens to the population as t increases without bound?
Answer by Nate(3500) About Me  (Show Source):
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a) Find the population in the year 2006.
P%28t%29=+++240%2F5+%2B+54.99e%5E%280.0208t%29
P%28t%29=+++240%2F5+%2B+54.99e%5E%280.0208%282006+-+1997%29%29
P%28t%29=+++48+%2B+54.99e%5E%280.0208%289%29%29
P%28t%29=+++114
b) In what year will the population reach 24 million?
P%28t%29=+++240%2F5+%2B+54.99e%5E%280.0208t%29
24000000=+++48+%2B+54.99e%5E%280.0208t%29
23999952=+54.99e%5E%280.0208t%29
23999952=+54.99e%5E%280.0208t%29
ln%2823999952%2F54.99%29+=+%280.0208t%29
ln%2823999952%2F54.99%29%2F0.0208+=+t
624.35+=+t
c) What happens to the population as t increases without bound?
The population increases as the time increases.