A computer virus nicknamed the Sapphire Worm spread throughout the internet on January $25,2003.$

Studies suggested that during the first few minutes, the population of infected computer hosts increased

at a rate that is proportional to the number of uninfected computers connected to the internet, where

the proportionality constant is $0\mathrm{.}0815.$ Further, suppose that only $10,000$ computers were connected

to the internet and at time $t=0($measured in seconds$),6$ computer hosts were infected answer the

following questions: