A certain antibiotic reduces the number of bacteria in your body by 10% each does. a)If four does of the antibiotic are taken, what percent of the original bacterial population is left?

I think the formula is supposed to be tn=100(9/10)^-1, but when i substituted 1 into it, the answer is wrong.

sorry i subbed 10 into it, and it was wrong.

sorry i meant 4

It should be

t(n) = 100(.9)^n

so if n=4
t(4) = 100(.9)^4 = 65.61

To determine the percent of the original bacterial population left after taking four doses of the antibiotic, we can start by considering the percentage reduction caused by one dose.

Since each dose reduces the bacterial population by 10%, the remaining bacterial population after one dose is 100% - 10% = 90% of the original population.

After taking the second dose, we have another 10% reduction in bacterial population. Since we start with 90% of the original population after the first dose, the remaining population after the second dose is 90% - 10% = 80% of the original population.

We can repeat this process for the third and fourth doses:

- After the third dose, we have 80% - 10% = 70% of the original population remaining.
- After the fourth dose, we have 70% - 10% = 60% of the original population remaining.

Therefore, after four doses of the antibiotic, 60% of the original bacterial population is left.

The formula tn=100(9/10)^n you mentioned is used for calculating the remaining percentage after 'n' doses. However, in this case, you want to calculate the overall percentage remaining after four doses, which is a one-time calculation. By manually calculating the reduction after each dose and updating the population, we arrive at the answer of 60% remaining.