Virus

We have a virus that lives one hour. Every half hour produces two child viruses. What will be the living population of the virus after 10 hours?

Final Answer:

x =  578272256

Step-by-step explanation:

$$\begin{gathered} 0.0h\dots n=1 \\ 0.5h\dots n=1+2-0=3 \\ 1.0h\dots n=3+6-1=8 \\ 1.5h\dots n=8+16-2=22 \\ 2.0h\dots n=22+44-6=60 \\ 2.5h\dots n=60+120-16=164 \\ 3.0h\dots n=164+328-44=448 \\ 3.5h\dots n=448+896-120=1224 \\ 4.0h\dots n=1224+2448-328=3344 \\ 4.5h\dots n=3344+6688-896=9136 \\ 5.0h\dots n=9136+18272-2448=24960 \\ 5.5h\dots n=24960+49920-6688=68192 \\ 6.0h\dots n=68192+136384-18272=186304 \\ 6.5h\dots n=186304+372608-49920=508992 \\ 7.0h\dots n=508992+1017984-136384=1390592 \\ 7.5h\dots n=1390592+2781184-372608=3799168 \\ 8.0h\dots n=3799168+7598336-1017984=10379520 \\ 8.5h\dots n=10379520+20759040-2781184=28357376 \\ 9.0h\dots n=28357376+56714752-7598336=77473792 \\ 9.5h\dots n=77473792+154947584-20759040=211662336 \\ 10.0h\dots n=211662336+423324672-56714752=578272256 \\ x=578272256 \end{gathered}$$

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