Unbeknownst to the crew members and themselves, 15 passengers who boarded an oce

Question

Unbeknownst to the crew members and themselves, 15 passengers who boarded an ocean liner on a luxury cruise were carriers for a virulent strain of influenza. Given that the flu spread aboard the ship at the rate of 20 new infected individuals per day and that the function f(t)=e^?0.02t determines the portion of newly infected passengers that still have the flu at time tt in days, then find the number of people with the flu on day 7 of the cruise.
Note! Round your decimal answer down to the number of completely infected people.

Explanation / Answer

Initially 15 passengers had it, and each day 20 passengers were infected by it;
Thus, on day 7 of the cruise, the following number of passengers still had the flue
= 15 + 20 e-0.12 + 20 e-0.1 + 20 e-0.08 + 20 e-0.06 + 20 e-0.04 + 20 e-0.02 + 20 e0
= 15 + 18 + 18 + 18 + 19+ 19 + 20 + 20 = 147

Thus, 147 people had the fly on day 7 of the cruise
Note: here we assume that the initial 15 passegners with the flu are permanent carriers and they have the flu throughout

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