Trying to set these equations up

[B-randon]

I've been working on math this morning, and these two equations I can't figure out. I have a test tomorrow and want to understand how to set them up in case theyre on the test.
Equation 1
Uranium 235 is used as fuel for some nuclear reactors. It has a half-life of 710 million years. How long will it take 10 grams of uranium 235 to decay to 1 gram? --- answer is 2,360 million years



Equation 2
You are trying to determine the half-life of a new radioactive element you have isolated. You start with 1 gram, and 2 days later you determine that it has decayed down to 0.7 grams. What is its half-life? --- answer is 3.89 days


I've been trying various ways of setting these up with pe^rt and A(.999879)^t and simplifying with logs to no avail. If someone can help me please do!

 

[HallsofIvy]

Where did you get ".999879"? The one thing that is directly given in each problem is "A".

 

[B-randon]

Where did you get ".999879"? The one thing that is directly given in each problem is "A".

It's a general equation that the book gives. The entire thing reads C(t) = A(0.999879)^t

 

[daveb]

The general form of the equation would be N(t) = N(0)e^-t*ln2/T, where T is the half-life, and N(0) is the number of atoms at time t = 0. So for each one, you have all the information you need.

 

[B-randon]

The general form of the equation would be N(t) = N(0)e^-t*ln2/T, where T is the half-life, and N(0) is the number of atoms at time t = 0. So for each one, you have all the information you need.

How would you set it up though?? I know I have all the information I just can't figure out where to put the information. For the first equation if I put 0 in for t the equation doesn't work out...if I put e^{-(10)*ln2/710} that doesn't work either.

 

[B-randon]

After a lot of hard work, I finally managed to figure out equation one.

I realize now daveb gave me the equation, but I didn't understand it.

So the equation would read: 1/10 = e^-([ln2]/710)t => ln(1/10) = -([ln2]/710)t => t = ln(1/10)/-([ln2]/710) = 2,360



I still am trying to figure out equation 2 but am confused

 

[eumyang]

I still am trying to figure out equation 2 but am confused

Use the equation that daveb gave again:
N(t) = N(0)e^-t*ln2/T

You're given that if t = 2, N(t) = 0.7. Solve for T. (While he said that N(0) = number of atoms at t = 0, it doesn't have to be in terms of atoms. It could be in terms of moles, or grams.)

 

[B-randon]

Use the equation that daveb gave again:
N(t) = N(0)e^-t*ln2/T

You're given that if t = 2, N(t) = 0.7. Solve for T. (While he said that N(0) = number of atoms at t = 0, it doesn't have to be in terms of atoms. It could be in terms of moles, or grams.)

THANK YOU! I never even thought of setting it up like that. I just get confused because there's so many equations, and it isn't explained thoroughly enough in class, as well as the examples the book gives aren't very helpful.