A bacteria colony exponentially grows with time. After just 2 hours, there are 4800 of them, and after 4 hours, there are 19200. How many were there to begin with?
Exponential law. N(t) = N_0exp(kt), where N(t) is the no. of bacteria at time t, N_0 is the initial no. of bacteria, t is time and k is a growth constant.
N(2) = 4800 => N_0exp(2k) = 4800 -------(1)
N(4) = 19200 => N_0exp(4k) = 19200 -------(2)
Divide (2)/(1):
exp(4k)/exp(2k) = 4
exp(2k) = 4
Put that back into eqn 1.
N_0*4 = 4800
Hence N_0 = 1200 (this is the number of bacteria at the start).
Comments
Exponential law. N(t) = N_0exp(kt), where N(t) is the no. of bacteria at time t, N_0 is the initial no. of bacteria, t is time and k is a growth constant.
N(2) = 4800 => N_0exp(2k) = 4800 -------(1)
N(4) = 19200 => N_0exp(4k) = 19200 -------(2)
Divide (2)/(1):
exp(4k)/exp(2k) = 4
exp(2k) = 4
Put that back into eqn 1.
N_0*4 = 4800
Hence N_0 = 1200 (this is the number of bacteria at the start).