Question

a research lab is to begin experiments with a bacteria that doubles every 4 hours. the lab starts with 200 bacteria. a. how many bacteria will be present at the end of 12th hour? b. how many bacteria will be present at the end of one day? please answer this​

Answer 1

A) 1600 bacteria

B) 12800 bacteria

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