Math problem

Question

A bacteria culture contains 1200 bacteria initally and increases by a factor of 1.5 every hour. Find a function to model their growth and predict the number of bacteria after 12 hours using your function.

Answer 1

We began with 1200 bacteria, and that amount is increased by 1.5 (that is growth of 50%) each hour.

 

bacterial growth is an exponential function given by the formula y = a (1+r)^t

 

where a = the initial amount, r = the growth rate, and t = the number of time intervals.

 

in this case, we have y = 1200 · (1.5)¹²

that number will be about 155,000

 

On this subject, you might want to look at http://www.textbookofbacteriology.net/growth_3.html

 

Exponential growth is not a perfect model of bacterial growth by binary fission, due to the fact that bacterial growth is no synchronized, but it is the appropriate model to use.