The​ half-life of a drug in the bloodstream is 9 hours. What fraction of the original drug dose remains in 12 ​hours?

amount = 1(1/2)^(12/9) =

Ah, the half-life of a drug. It's like a celebrity relationship, just with significantly more math. Now, let's get cracking on solving this puzzle!

If the half-life of the drug is 9 hours, that means that after 9 hours, half of the drug dose will remain. So, after 9 hours, we're left with 50% of the original dosage.

Now, let's move on to the next step. We want to know what fraction of the original drug dose remains in 12 hours. So, if after 9 hours we're left with 50%, what do you think happens in the next 3 hours?

Well, if we use our math skills, we can predict that in another 3 hours, the drug will half its remaining dose. So after 12 hours, we're left with 50% of the remaining 50% from the previous step.

Now, let's calculate the final result of this mathematical comedy routine.

50% of 50% is... (drumroll, please)... 25%!

Therefore, after 12 hours, approximately 25% of the original drug dose remains. It's like the drug's version of disappearing into the witness protection program, without the cool fake mustache!

To determine what fraction of the original drug dose remains in 12 hours, we need to calculate the number of half-lives that have passed in that time frame.

The formula to calculate the number of half-lives is given by:
Number of half-lives = time elapsed / half-life

In this case, the time elapsed is 12 hours, and the half-life of the drug is 9 hours. Plugging in these values, we get:
Number of half-lives = 12 hours / 9 hours

Calculating this, we find that the number of half-lives is approximately 1.33.

To determine the fraction of the original drug dose that remains, we use the formula:
Fraction remaining = (1/2)^(number of half-lives)

Plugging in the value for the number of half-lives, we get:
Fraction remaining = (1/2)^1.33

Calculating this, we find that the fraction remaining is approximately 0.549.

Therefore, approximately 54.9% of the original drug dose remains in 12 hours.

To determine the fraction of the drug dose remaining after 12 hours, we need to understand the concept of half-life.

The half-life of a drug is defined as the time it takes for half of the drug to be eliminated from the bloodstream. In this case, the half-life of the drug is 9 hours.

To find the fraction of the drug dose remaining after a certain time period, divide the time period by the half-life and raise it to the power of the number of half-lives that have passed.

In this case, we want to find the fraction remaining after 12 hours, so we divide 12 by the half-life of 9 to get:

12 hours / 9 hours = 1.33.

The number 1.33 represents the number of half-lives that have passed. Since we can't have a fraction of a half-life, we need to round down to the nearest whole number. In this case, we would have 1 whole half-life.

Now, we raise the fraction to the power of the number of half-lives:

(1/2) ^ (number of half-lives) = (1/2) ^ 1 = 1/2 = 0.5.

Therefore, after 12 hours, approximately half of the original drug dose remains.