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
Answer:
The size of the bacteria colony after 20 days = 9720
Step-by-step 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
