Question

Jimmy Lee has a fungal infection in his armpit. He was prescribed a medicine that guarantees a 29% decrease in the fungus every day. About how many days will it take the medication to eradicate the fungus down to 1% of its original amount?

Answer 1

It will take approximately 2 days for the medication to eradicate the fungus down to 1% of its original amount.

Step-by-step explanation:

To calculate the number of days it will take for the medication to eradicate the fungus down to 1% of its original amount, we can use exponential decay. If the medication guarantees a 29% decrease in the fungus every day, we can represent this as a decay factor of 0.71 (100% - 29% = 71%).

Using the formula A = A0 * r^n, where A is the final amount (in this case, 1% of the original amount), A0 is the initial amount (100% of the original amount), r is the decay factor (0.71), and n is the number of days, we can solve for n.

0.01 = 1 * 0.71^n

Dividing both sides of the equation by 1, we get:

0.01/1 = 0.71^n

0.01 = 0.71^n

Next, take the logarithm of both sides using base 0.71:

log0.71(0.01) = log0.71(0.71^n)

Simplifying the equation:

-2 = n

Therefore, it will take approximately 2 days for the medication to eradicate the fungus down to 1% of its original amount.