Calculating Total Number of Live Viruses after 10 Seconds

[johncena]

Homework Statement

A virus give birth to 2 new virus in each second and life span of each virus is 5 seconds.The process of reproduction is continuous until the death of the virus.Initially there is one newly born virus at time t=0.Find the total number of live viruses just after 10 seconds.

Homework Equations

number of viruses born - number of viruses dead

The Attempt at a Solution

Number of born viruses = 1+2+4+8+...+1024
Number of viruses dead = 0x4+(1+2+4+...+64)

there fore, answer = 2⁷+2⁸+2⁹+2¹⁰

but the given answer is 3⁵(3⁵-1)
Nowhere near!

pls help...

 

[Dick]

Homework Statement

A virus give birth to 2 new virus in each second and life span of each virus is 5 seconds.The process of reproduction is continuous until the death of the virus.Initially there is one newly born virus at time t=0.Find the total number of live viruses just after 10 seconds.

Homework Equations

number of viruses born - number of viruses dead

The Attempt at a Solution

Number of born viruses = 1+2+4+8+...+1024
Number of viruses dead = 0x4+(1+2+4+...+64)

there fore, answer = 2⁷+2⁸+2⁹+2¹⁰

but the given answer is 3⁵(3⁵-1)
Nowhere near!

pls help...

3^5*(3^5-1)=58806. Even if no viruses die, that's way to big be the answer after 10 seconds. If that's the given answer, there is something wrong with it. But your answer isn't right either. Dead viruses don't reproduce.

 

[johncena]

Sir, i can't get you ... can you explain a bit more?
you mean that no more viruses reproduce after 5 seconds?

 

[Dick]

Sir, i can't get you ... can you explain a bit more?
you mean that no more viruses reproduce after 5 seconds?

I mean that the ones that have died don't contribute to the count of born ones. Try working this out as a table. At t=4 you have 16. At t=5 you have 32, then you remove the old one so you get 31. How many at t=6?

 

[johncena]

Ohhhh...i missed that point...

thanks sir...you was very helpful...