how many bacteria will there be at the same time tomorrow, assuming none of these bacteria die in the meantime?

Question

A culture of bacteria doubles every hour. If there are 100 bacteria at the beginning, how many bacteria will there be at the same time tomorrow, assuming none of these bacteria die in the meantime?

Answer 1

After one hour we the number of bacteria doubles (2n).  After two hours the number of bacteria doubles again (2x2n=4n).  After three hours the number of bacteria doubles again (2x2x2n=8n).  so we have a geometric series of 2^t, where t represents the number of hours from the beginning.  So out equation looks like

 

2^tn = number of bacteria at time t

 

2²⁴(100) = number of bacteria after 24 hours when starting with 100