Question

It is observed that a certain bacteria culture has a relative growth rate of 15% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 5% per hour. The initial number of bacteria in the culture is 24. Find the projected population after 24 hours for the following conditions. (Round your answers to the nearest whole number.)

Answer 1

Answer: 110 in the presence of no antibiotic, 53 in the presence of an antibiotic

Step-by-step explanation:

So first we are told the growth rate of a bacteria culture is 15% and the number of bacteria in the culture is 24

So we find 15% of 24

15/100 x 24 = 18/5

So 18/5 bacteria is produced every hour, then for 24hours

18/5 x 24 = 86.4

The number of bacteria is already 24 as said

So altogether

86.4 + 24 = 110.4 approximately 110

Then, for the presence of antibiotic, the growth rate is 5%

So 5% of 24

5/100 x 24 = 6/5

So 6/5 bacteria is produced every hour

For 24hours

6/5 x 24 = 28.8

Initial culture = 24

Final culture = 24 + 38.8 = 52.8 approximately 53