SOLUTION: In a town whose population is 3500, a disease creates an epidemic. The number of people N infected after t days after the disease has begun, is given by the function N(t) = 3500

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Question 190667: In a town whose population is 3500, a disease creates an epidemic. The number of people N infected after t days after the disease has begun, is given by the function
N(t) = 3500/1 + 19.9e^-0.6t
Find the number of people infected after 15 days. Round-off your answer to the nearest unit, i.e. with no decimals.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
N%28t%29=%283500%29%2F%281%2B19.9e%5E%28-0.6t%29%29 Start with the given function.


N%2815%29=%283500%29%2F%281%2B19.9e%5E%28-0.6%2815%29%29%29 Plug in t=15.


N%2815%29=%283500%29%2F%281%2B19.9e%5E%28-9%29%29 Multiply -0.6 and 15 to get -9


N%2815%29=%283500%29%2F%281%2B19.9%280.000123%29%29 Raise "e" to the negative 9th power to get 0.000123


N%2815%29=%283500%29%2F%281%2B0.00245%29 Multiply 19.9 and 0.000123 to get 0.00245


N%2815%29=%283500%29%2F%281.00245%29 Add 1 to 0.00245 to get 1.00245


N%2815%29=3491.445 Divide


So rounding to the nearest whole number (since 0.445 of a person doesn't make sense), we get 3,491 people.

So after 15 days, about 3,491 people are infected.