It is observed that a certain bacteria culture has a relative growth rate of 16% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 6% per hour. The initial number of bacteria in the culture is 21. Find the projected population after 24 hours for the following conditions.
(a) No antibiotic is present, so the relative growth rate is 16%.
(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 6%.

Question

It is observed that a certain bacteria culture has a relative growth rate of 16% per hour, but in the presence of an antibiotic the relative growth rate is reduced to 6% per hour. The initial number of bacteria in the culture is 21. Find the projected population after 24 hours for the following conditions.
(a) No antibiotic is present, so the relative growth rate is 16%.
(b) An antibiotic is present in the culture, so the relative growth rate is reduced to 6%.

anonymous · Answer

to increase a number by $16\%$ multiply it by $100\%+16\%=116\%=1.16$

anonymous · Answer

to do it 24 times, multiply it by $$1.16^{24}$$

anonymous · Answer

you will need a calculator to compute $$21\times 1.16^{24}$$