Application of exponential and logarithmic functions

Question

Bacteria growing in a petri dish quadruple every 2 hours. If the sample has 18 bacteria in the dish initially,(a) write a function to describe the population at time t. Also,(b) find the population at t = 8 hours and,(c) t = 16 hours

Answer 1

n = n0*2^(t/td)

where: n is the total number of sample bacteria
n0 is the initial number of sample bacteria = 18 bacteria
td is the time the bacteria doubles = 2 hr
t is the final time (hr)
'2' represents 'it doubles'

b) n = 18*2^(8 hr/2 hr) 

n = 18*2^(4) = 18*16= 288 bacteria after 8 hrs

c) n = 18*2^(16 hr/2 hr) = 18*2^(8) =18*256 = 4608 bacteria after 16 hrs