# exponentail growth

• Dec 3rd 2008, 07:37 PM
Steph07
exponentail growth
Given: There are 7 billion, that is, 7*109
people on Earth. If a bird flu virus starts
with one person and within 5 days two
people are infected, then each of those two
people in 5 days infects 2 people each,
and so on, how many days before everyone
on earth is infected?
Hint: Geometric series and logarithms
• Dec 3rd 2008, 08:06 PM
terr13
Essentially it is saying that every 5 days, the population that is infected will double. How long until it reaches 7,000,000,000.
The equation is $N(t) = N_0 e^(rt).$, where N_0 is the initial population (1 in this case), r is the rate of which it expands, and t is the time. You want to find when this equals 7 billion, so enter 7 billion on the other side and then solve for the time t. e is a constant, about 2.71.
• Dec 3rd 2008, 08:20 PM
Steph07
oh im sry that 10^9 power
• Dec 3rd 2008, 08:24 PM
Steph07
I am kinda confused.. so what would t and r be? how do i get that? and N_0 would be sub. as 1 ?