Epidemic A virus is spreading by human to human physical con

Epidemic! A virus is spreading by human to human physical contact and turning all into zombies. The amount of zombies present is exponentially increasing and modeled by the function z(t) = 15,000e^0.05t, where t represents the days since the first infection. Find the number of zombies (a) at the beginning of the epidemic (b) after 10 days (c) after 4 weeks

Solution

The number of zombies, z(t) = 15000e^0.05t where t is the number of days since the first infection.

(a)   At the beginning of the epidemic t = 1( t can not be zero because, then there is no infection). Therefore, z(1) = 15000e^0.05 = 15000*1.05127109638= 15769( on rounding off to the nearest whole number)

(b) After 10 days, z(10) = 15000e^0.05*10 = 15000e^0.5 = 15000*1.6487212707= 24731( on rounding off to the nearest whole number)

(c ) After 4 weeks, t = 4*7 = 28, therefore z(28) = 15000e^0.05*28= 15000e^1.40= 15000*4.05519996684= 60828( on rounding off to the nearest whole number)