If a 25 mg sample of radioactive material decays to 18.4 mg in 5 years, how long will it take the sample to decay to 20.5 mg?
25*e^-5k = 18.4
So, k = ln(18.4/25)/-5 = 0.0613
So, now just solve for t in
25*e^-.0613t = 20.5
bcx xb
To determine the time it takes for a radioactive sample to decay to a specific amount, we can use the concept of half-life. The half-life is the time it takes for half of the sample to decay.
In this case, we know that the initial sample size is 25 mg, and it decays to 18.4 mg after 5 years. We can calculate the half-life by finding the time it takes for half of the initial sample (25 mg / 2 = 12.5 mg) to decay to 18.4 mg.
So, the difference between the initial sample size and the decayed sample size is 25 mg - 18.4 mg = 6.6 mg. This represents half of the initial sample size, so the half-life is 5 years.
Now, to find out how long it will take the sample to decay to 20.5 mg, we can determine the difference between the initial sample size and the desired decayed sample size: 25 mg - 20.5 mg = 4.5 mg.
Since the half-life is 5 years, we can calculate how many half-lives it would take for the sample to decay by 4.5 mg: 4.5 mg / 6.6 mg (half of the initial sample size) = 0.68 half-lives.
Since we can't have a fraction of a half-life, we can round up to the nearest whole number. Therefore, it will take approximately 1 half-life for the sample to decay to 20.5 mg.
Therefore, it will take approximately 5 years for the sample to decay to 20.5 mg.