SOLUTION: The logistic growth function below describes the number of people, f(t), who became ill with the flu “t” weeks after its initial outbreak in a particular community. f(t)=200,000/1

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The logistic growth function below describes the number of people, f(t), who became ill with the flu “t” weeks after its initial outbreak in a particular community. f(t)=200,000/1      Log On


   



Question 1058723: The logistic growth function below describes the number of people, f(t), who became ill with the flu “t” weeks after its initial outbreak in a particular community.
f(t)=200,000/1+2000e^-t
(a) How many people became ill with the flu when the epidemic began? (round to the nearest whole number) Answer: 100
(b) How many people were ill by the end of the fourth week? (round to the nearest whole num-ber)
(c) What is the limiting size of the population that became ill? EXPLAIN in words please

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28t%29+=+200000%2F%28+1+%2B+2000%2Ae%5E%28-t%29+%29+
(a)
+f%280%29+=+200000%2F%28+1+%2B+2000%2Ae%5E%28-0%29+%29+
+f%280%29+=+200000%2F%28+1+%2B+2000+%29+
+f%280%29+=+99.95+
round off to +100+
(b)
+f%284%29+=+200000%2F%28+1+%2B+2000%2Ae%5E%28-4%29+%29+
+f%284%29+=+200000%2F%28+1+%2B+2000%2A.0183156+%29+
+f%284%29+=+200000%2F37.631278+
+f%284%29+=+5314.72+
5,315 people were ill by the end of the 4th week
(c)
Let +t+ approach infinity
+e%5E%28-t%29+ will approach zero, so
+f%28inf%29+=+200000%2F%28+1+%2B+0+%29+
+f%28inf%29+=+200000+
The limit is that all of them become ill
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