What is the process of solving this question?

Question

I have a handful of questions like these that I have to do and if someone can walk me through one of them, it would really help me get them done.

A scientist begins with 100 mg of a radioactive substance. After 2 hours, it has decayed to 60 mg. How long after the process began will it decay to 10 mg?

Answer 1

Let P=100mg

 

t=2

 

A=60mg

 

A=P*e^kt

 

60=100*e^2*k

 

60/100=e^2*k

 

Taking natural logs on both sides

 

ln (0.6) = 2k

 

k= (ln(0.6)/2)

 

k=-0.5108/2 = -0.2554

 

Now we know the value of k which is the decay rate

 

Now we need to find out the time when the process decay to 10 mg

 

A=P*e^kt

 

10=100*e^-0.2554*t

 

Taking natural logs on both sides

 

ln (10/100)=-0.2554*t

 

Therefore

 

t= (-2.3025/-0.2554)

 

t=9.02 hrs

 

If you have any other problems feel free to contact me and I can help you out with other problems.

 

Answer 2

A = Pe^rt

60 = 100e^2r

0.6 = e^2r

ln 0.6 = 2r

 

Can you solve for r and answer the question?