So me and my friend were having an argument.

A friend of mine told me that if the entire population of China was to line up single file and walk past you, with the growth rate of China, the line would never end. I disagreed. Here are the "facts."

Population of China (2008): 1,325,639,982.
Growth Rate: .78%
Average walking speed: 3mi/hr

We both agreed that every 2 feet would include a person, i.e. if 3 people walked by they could be contained in a 6foot span. Also, I told him that at most it takes 1 year for a child to learn to walk (this may be overkill so I will give him the benefit of the doubt and assume they can start walking at birth.)

So I came up with this equation.

f(x)= 1325639982*(1.0078)^x - 69116400*x. (Where 1325639983*(1.0078)^x represents the population and 69116400*x represents the number of people that have walked past you, both in x years.)

We solve for f(x)=0. The problem is I can't solve it.
I also thought there may be some way to do it compounded.

So I ask these two things:
1. Does that equation look correct?
2. How do I go about solving it?

Thanks peoples!

The equation aside, I have heard this one before. It dates back to an old Ripley's Beieve It Or Not, I believe.

Let's say that 1 person walks by you every second. It would take a little over 42 years for all those people to walk by.

More than enough time for those in the back to propagate and continue the never ending line.

Of course, it is a silly and impractical little chestnut, but the point is that 1 billion is a huge number.

Your equation assumes that newborns will always be to the side that the people are coming from.

The "gigapede" can have reproduction taking place among the people that have walked past you,
as well as among those walking towards you.

Then these newborns are being rushed to the other side of the gigapede after birth ??
Very rough on the kids.

That is if arrangements have been made for procreating and giving birth "on the walk".

Your equation is hitting zero at around the 380 year mark.
You will be right if your life extension program is successful for you.

Another way to make calculations is to work it out as you do for loans.
Imagine the people are dollars.
The people who have walked by are your loan repayments
and the newborns are the bank's interest.
How many years will it take for you to pay off the loan at 0.78% interest on your $1.33 billion loan ?
Same calculations unfortunately.

You don't have to find f(x)=0.
Just try a few x's such as f(50), f(100) and so on, until f(x) goes negative.
If f(x) is positive, it means there's still stragglers at the back of the queue.