Bacteria colonies can triple in size every 4 days. if you start with 40 bacteria microorganisms, how large would the colony be after 20 days?

Assuming the reaction is of 1st order, we can start using the formula for rate of 1st order reaction:

dN / dt = k * N

Rearranging,

dN / N = k dt

Where N = amount of sample, k = rate constant, t = time

Integrating the equation from N = Ni to Nf and t = ti to tf will result in:

ln (Nf / Ni) = k (tf - ti)

Since k is constant, we can equate to situations. Situation 1 is triple in size every days, situation 2 is after 20 days.

ln (Nf / Ni) / (tf - ti) = k

ln (3Ni / Ni) / 4 = ln (Nf / 40) / 20

Calculating for Nf,

Nf = 9,720 bacteria