Application of exponential and logarithmic functions

Question

Bacteria growing in a petri dish double every 30 minutes. If the sample has 10 bacteria in the dish initially,(a) write a function to describe the population at time t. Also,(b) find the population at t = 4 hours and,(c) t = 6 hours

Answer 1

a)

      n = n0*2^(t/td)

 

where:  n is the total number of sample bacteria

           n0 is the initial number of sample bacteria = 10

            td is the time the bacteria doubles (hr)

            t is  the final time (hr)

           '2' represents 'it doubles'

 

b)  n = 10*2^(4 hr/0.5 hr)     Note:  0.5 hr equal 30 min

 

     n = 10*2^(8) = 10*256 = 2560 bacteria after 4 hrs

 

c)  n = 10*2^(6/0.5) = 10*2^(12) =10*4096 = 40,960 bacteria after 6 hrs