MathBench > Population Dynamics

Frank's Football Fiasco

Some more practice

There are fast and exact ways to solve these kinds of problems (if you remember your advanced algebra), and there are slower and less exact ways (if you don't). Either way is fine here, although the hints will only be for the non-advanced-algebra route.

threeWhat if exactly 3 meningococci surrived the initial onslaught of Frank's immune system? In that case, how long would it be before the critical level of 2.5 million organisms was reached?

(To make this problem interactive, turn on javascript!)

I think I have the answer: between 19 and 20 generations

 

The guess-and-try method is fine, if a little slow. However, if you understand how doubling works, you can make some intelligent guesses and speed up your answers. For example, if 2.5 million cells require 21 generations, what would 1.25 million cells require?

With that in mind, try the next problem.

girlWhat if Frank was a 10 year old girl with 2.5 liters of blood (as opposed to Frank-the-Flag-Footballer's 5 liters)? In that case, how many generations would it take to get to the lethal level?

(To make this problem interactive, turn on javascript!)

I think I have the answer: 20 generations

 

One last problem, just to make sure you've got it.

blood driveWhat if Frank had just given blood, losing about half a liter, plus his weakened immune system let 5 meningococci though? Poor Frank!

(To make this problem interactive, turn on javascript!)

I think I have the answer: 19 generations gives 2.6 million cells