Question

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?

Answer 1

The size of the bacteria colony after 20 days = 9720

Explanation:

The number of bacteria micro organism at the starting = 40

Now, The size of the bacteria colonies triple in size every 4 days

and we need to find the size of the bacteria colony after 20 days.

So, after 4 days the size of bacteria colony = 40 × 3

= 120

After 8 days, The size of the bacteria colony = 120 × 3

= 360

After 12 days, The size of the bacteria colony = 360 × 3

= 1080

After 16 days, The size of the bacteria colony = 1080 × 3

= 3240

After 20 days, The size of the bacteria colony = 3240 × 3

= 9720

Therefore, The size of the bacteria colony after 20 days = 9720

Answer 2

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