Question

A computer virus is infecting a large network. As each PC becomes infected, it infects two other PCs every 1.1 minutes.

Use the following formula y=a(b)^t/p

where

a=initial amount=1 computer

b=the growth factor= number of computers being affected periodically

t=time that has passed (this is what we must solve for)

p=period of growth or decay= given number of minutes in the time period

y=number of infected computers at the end How long until 15 million PCs are infected?

Please explain and show work. Thank you!

Answer #1

Answer :

Consider the following formula y=a(b)^t/p

where

a=initial amount=1 computer

b=the growth factor= number of computers being affected periodically = 2

t=time that has passed (this is what we must solve for)

p=period of growth or decay= given number of minutes in the time period = 1.1 min

y=number of infected computers at the end

So that y = 1*(2)^{t/1.1}

when y = 15 million = 15 x 10^{6} we find the value of t
= ?

15 x 10^{6} = 2^{t/1.1}

Apply logarithm on both sides

ln(15 x 10^{6}) = ln(2^{t/1.1})

ln(15 x 10^{6}) = (t/1.1)ln(2)

Multiply by (1.1)/ln(2) on both sides , we get

t =(1.1)( ln(15 x 10^{6})/ln(2))

= 26.2223

After 26.2223 minutes there will be 15 million infected PCs.

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