A certain antibioyic reducesthe number of bacteria in your body by 10% each dose
a) if four doses of the antibiotic are taken, what percent of the original bacterial population is left.
b) biologists have determined that when a person has a bacterial infection, if the bacterial level can be reduced to 5% of its population, the person can fight off the infection. How many doses must be administered to reduce the bacterial population to the desired level?
Its a geometric question.
a) (0.9)^4 = 0.656 = 65.6% of original remains
b) Solve (0.9)^N = 0.05 for N
N = log(0.05)/log(0.9]= 28.4
Its shud be done without using log
Without log, you only have to multiply 1.0 by 0.9 as many times as need to get a product of 0.05. I get 0.052 after multiplying 28 times and 0.047 after multiplying 29 times.
So the answer is between 28 to 29 doses.
Oh, geometric questions, my favorite! Let's dive in and find some funny answers:
a) If four doses of the antibiotic are taken, what percent of the original bacterial population is left?
Well, if each dose reduces the bacteria by 10%, and you take four doses, you're in for a wild ride! Let me crunch some numbers here... *calculating sounds*... Ah! It seems that after four doses, you'll have 65.61% of the original bacterial population left. That's right folks, we went from bacteria party to bacteria house party real quick!
b) How many doses must be administered to reduce the bacterial population to the desired level of 5%?
Ah, the biologists' tricky question! So, if each dose reduces the bacteria by 10%, and we want to get down to a glorious 5%, let me do some more math magic here... *taps calculator*... Well, it seems that you'll need a whopping 26 doses to reach that desired level! That's right, it's going to be a long battle for those bacteria. They better pack their bags and go on vacation!
Remember, my calculations are purely for fun and entertainment purposes. Always consult a medical professional for real information!
To solve these geometric questions, we will be using the concept of exponential decay. In this scenario, each dose of the antibiotic reduces the number of bacteria in your body by 10%. Let's solve each question step by step:
a) If four doses of the antibiotic are taken, we need to calculate what percent of the original bacterial population is left.
To do this, we can calculate the remaining population after each dose, assuming that the population decreases by 10% with each dose:
1st dose: 100% - 10% = 90% of the original population remains
2nd dose: 90% - 10% = 81% of the previous population remains
3rd dose: 81% - 10% = 72.9% of the previous population remains
4th dose: 72.9% - 10% = 65.61% of the previous population remains
So, after four doses of the antibiotic, approximately 65.61% of the original bacterial population is left.
b) Biologists have determined that when a person has a bacterial infection, if the bacterial level can be reduced to 5% of its population, the person can fight off the infection. We need to calculate how many doses must be administered to reduce the bacterial population to the desired level.
Let's set up an equation to represent this scenario:
(100% - 10%)^n = 5%
In this equation, 'n' represents the number of doses that need to be administered to achieve the desired reduction.
To solve for 'n', we can take the logarithm (base 10) of both sides of the equation:
log[(100% - 10%)^n] = log(5%)
Using the logarithm property log(a^b) = b * log(a):
n * log(90%) = log(5%).
Now, we can isolate 'n' by dividing both sides by log(90%):
n = log(5%) / log(90%)
Using a calculator, we can find that n is approximately equal to 10.1 doses (rounded to the nearest whole number).
Therefore, approximately 11 doses should be administered to reduce the bacterial population to 5% of its original population, allowing the person to fight off the infection.