SOLUTION: The function f(t) 30,000/1+20e^-1.5t describes the number of people, f(t), who have become ill with influenza t weeks after the initial outbreak in a town with 30,000 inhabitants.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The function f(t) 30,000/1+20e^-1.5t describes the number of people, f(t), who have become ill with influenza t weeks after the initial outbreak in a town with 30,000 inhabitants.       Log On


   



Question 1029823: The function f(t) 30,000/1+20e^-1.5t describes the number of people, f(t), who have become ill with influenza t weeks after the initial outbreak in a town with 30,000 inhabitants.
a. How many people became ill with the flu when the epidemic began?
b. How many people were ill by the end of the fourth week?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2Ae%5E%28-1.5t%29%29+
(a)
When the epidemic began, +t+=+0+, so
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2Ae%5E%28-1.5%2A0%29%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2Ae%5E0+%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2A1+%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+20+%29+
+f%28t%29+=+30000+%2F+21+
+f%28t%29+=+1428.57+
1,429 people became ill when
the epidemic began
-------------------------
(b)
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2Ae%5E%28-1.5%2A4%29+%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2Ae%5E%28-6%29+%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+20%2A.002479+%29+
+f%28t%29+=+30000+%2F+%28+1+%2B+.04958+%29+
+f%28t%29+=+30000+%2F+1.04958+
+f%28t%29+=+28582.86+
28,583 people were ill by the end
of the fourth week