a certain antibiotic redues the number of bacteria in your body by 10% each dse, if 4 doses of the antibiotic are taken, what percent of the original bacterial population is left
after 1st day .9 or 90% left
after 2nd day .9^2 or .81 or 81% left
after 3rd day .9^3 .......
etc
To determine the percent of the original bacterial population that is left after taking 4 doses of the antibiotic, we can use the concept of percentage decrease.
Each dose of the antibiotic reduces the number of bacteria in your body by 10%. So, after one dose, there will be 100% - 10% = 90% of the bacteria left.
To find the remaining bacteria after multiple doses, we need to calculate the percent remaining after each dose and multiply the results:
After 1 dose: 90% of the bacteria remains.
After 2 doses: The remaining 90% is reduced by another 10%, so there will be 90% * (100% - 10%) = 90% * 90% = 81% of the bacteria left.
After 3 doses: The remaining 81% is reduced by 10%, so there will be 81% * (100% - 10%) = 81% * 90% = 72.9% of the bacteria left.
After 4 doses: The remaining 72.9% is reduced by 10%, so there will be 72.9% * (100% - 10%) = 72.9% * 90% = 65.61% of the bacteria left.
Therefore, after taking 4 doses of the antibiotic, approximately 65.61% of the original bacterial population remains.