A research student is working with a culture of bacteria tha

A research student is working with a culture of bacteria that doubles in size every fifteen minutes. The initial population count was 2 bacteria. Write an exponential equation representing this situation. Use t to represent hours. P(t) = To the nearest whole number, what is the population size after 2 hours? bacteria

Solution

dN/dt = kN this is the first order kinetics

if i solve this equation i will get the N = N₀exp(kt) here N₀ is the initial population count of bacteria

k= rate constant , t= time taken in hours

4= 2exp(kt)

exp(kt)= 2

k = ln2/t and t= 0.25 hours

k = 4ln2

N =2exp(kt) where k= 4ln2

population size after 2 hours

N= 2exp(4ln2*2)

N= 512 bacterias