Answer:
A) 1600 bacteria
B) 12800 bacteria
Step-by-step explanation:
We are told that the bacteria doubles every 4 hours.
Now, if the amount of bacteria is X, it means that for 4 hours, it becomes 2X and after 8 hours it becomes 2(2X)
For 12 hours, it becomes; 2 × (2(2X))
This means that for 12 hours, it becomes 2 × (2(2X)) = 8X
A) Since the lab starts with 200 bacteria, after 12 hours, it has;
N_12 = 8 × 200.
N_12 = 1600 bacteria
B) From above, we have seen that after t hours, where t is a multiple of 4, the number of bacteria is;
N_t = [2^(¼t - 1)] × (2X)
Where X is initial amount of bacteria.
Thus, after a day which is 24 hours, we have;
N_24 = 2^(¼(24) - 1) × 2X
N_24 = 2^(5) × 2X
Where X is 200, N_24 = 32 × 2(200) = 12800 bacteria
