At the beginning of an experiment, a scientist has 360 grams

[qbkr21]

At the beginning of an experiment, a scientist has 360 grams of radioactive goo. After 105 minutes, her sample has decayed to 22.5 grams.

Questions:

1. What is the half-life of the goo in minutes?

2. Find a formula for G(t), the amount of goo remaining at time "t". G(t)=?

3. How many grams of goo will remain after 74 minutes:?

Thanks for the help. I do not know any of the formulas to calculate this, however I am excellent with logs. Again thanks for taking the time to look at this...

 

[galactus]

Find k. You need that first.

Use \(\displaystyle A=A_{0}e^{kt}\)

Given 22.5 grams remaining after 105 minutes from an initial 360 grams.

\(\displaystyle 22.5=360e^{k(105)}\)

Solve for k.

Once you have that, use it to find 1/2 life and the last part of the problem:

\(\displaystyle \frac{A_{0}}{2}=A_{0}e^{kt}\Rightarrow{t=\frac{ln(\frac{1}{2})}{k}\)

 

[qbkr21]

I solved for K and got -.026406=K; where do I go from here?

I have never delt with a half-life before I am new to this concept...


Thanks

 

[qbkr21]

ok so I got the half life but what about formula G(t) and how would I calculate it after 74 min? Just by substituting in 74 for "t"?

 

[galactus]

Just as it says, a half-life is when there is half left.

After you have k, plug 74 in for t and k in for k. That will give you how

much is left after 74 minutes.