How do i solve for time "t" in the equation for radioactive decay.

[imitch119]

My environmental science teacher gave us a set of problems to solve without teaching us the material to see if we could figure it out on our own. well, I've tried for hours on this last one and i need some serious help. heres the question.

An igneous rock originally has 3 grams of uranium-238 in it. when dated, the rock only contains 1.8 grams. what are the parent and daughter concentrations (in percentages) and what is the age?

to determine age, i think i must use the equation A=Ao*(1/2)^t/h and solve for t.
is this correct? How do i do this? this math is wayyy over my head. i would greatly appreciate anyones imput.
thanks.

 

[Ishuda]

My environmental science teacher gave us a set of problems to solve without teaching us the material to see if we could figure it out on our own. well, I've tried for hours on this last one and i need some serious help. heres the question.

An igneous rock originally has 3 grams of uranium-238 in it. when dated, the rock only contains 1.8 grams. what are the parent and daughter concentrations (in percentages) and what is the age?

to determine age, i think i must use the equation A=Ao*(1/2)^t/h and solve for t.
is this correct? How do i do this? this math is wayyy over my head. i would greatly appreciate anyones imput.
thanks.

Do you know what A, Ao, t and, h represent? If you had an equation
4 = 2^t/7
would you know how to solve for t?

To answer the daughter/parent question, you will have to know what the daughter and parent are.

I suggest some reading:
For a discussion of parent/daughter: http://en.wikipedia.org/wiki/Isochron_dating
For a discussion on half life: http://en.wikipedia.org/wiki/Half-life
For a discussion on U238: http://en.wikipedia.org/wiki/Uranium-238

 

[stapel]

My environmental science teacher gave us a set of problems to solve without teaching us the material to see if we could figure it out on our own. well, I've tried for hours on this last one and i need some serious help. heres the question.

An igneous rock originally has 3 grams of uranium-238 in it. when dated, the rock only contains 1.8 grams. what are the parent and daughter concentrations (in percentages) and what is the age?

Maybe this information is covered in whatever math course is the prerequisite for this science course...? In any case, you can find plenty of lessons online, such as the listing provided here.

 

[HallsofIvy]

The inverse operation to exponentiation is the logarithm: \(\displaystyle log_a(a^x)= x\) and \(\displaystyle a^{log_a(x)}= x\).

 

[imitch119]

A=amt after time
Ao=starting amt
h=half life
t=time gone by

i know all the info except t. i have never taken a course that went over any of this. what i need to know is how do i go about solving for t? like, what would be the equation for t=...?

 

[imitch119]

is this the correct way to solve this problem?

A=1.8g
Ao=3g
h=4.5 bil yr

A=Ao*(1/2)^t/h

1.8=3*(1/2)^t/4.5bil

then do i take (1/2)log(4.5bil) and multiply by three then divide 1.8 by the answer? I'm not sure the correct order of operations when i have an exponent being devided by another unknown exponent. does that make sense? its hard for me to explain my thought process.

 

[imitch119]

My environmental science teacher gave us a set of problems to solve without teaching us the material to see if we could figure it out on our own. well, I've tried for hours on this last one and i need some serious help. heres the question.

An igneous rock originally has 3 grams of uranium-238 in it. when dated, the rock only contains 1.8 grams. what are the parent and daughter concentrations (in percentages) and what is the age?

to determine age, i think i must use the equation A=Ao*(1/2)^t/h and solve for t.
is this correct? How do i do this? this math is wayyy over my head. i would greatly appreciate anyones imput.
thanks.

is this the correct way to solve this problem?

A=1.8g
Ao=3g
h=4.5 bil yr

A=Ao*(1/2)^t/h

1.8=3*(1/2)^t/4.5bil

then do i take (1/2)log(4.5bil) and multiply by three then divide 1.8 by the answer? I'm not sure the correct order of operations when i have an exponent being devided by another unknown exponent. does that make sense? its hard for me to explain my thought process.

 

[Ishuda]

You need to learn/remember the rules for taking logarithms
log(a * b) = log(a) + log(b)
log(a / b) = log(a) - log(b)
log (a^b) = b log(a)

So, for example log(3*(1/2)^(t/4.5)) = log(3) + log((1/2)^(t/4.5))

 

[imitch119]

You need to learn/remember the rules for taking logarithms
log(a * b) = log(a) + log(b)
log(a / b) = log(a) - log(b)
log (a^b) = b log(a)

So, for example log(3*(1/2)^(t/4.5)) = log(3) + log((1/2)^(t/4.5))

Okay so how do i solve this for t? i don't quite understand.
is it: log(3)+log((1/2)^4.5bil) then divide by 1.8 to get the t alone?

 

[HallsofIvy]

You said

My environmental science teacher gave us a set of problems to solve without teaching us the material to see if we could figure it out on our own.

Then you should not worry about how to do it and just let your teacher know you can't!

 

[Ishuda]

Okay so how do i solve this for t? i don't quite understand.
is it: log(3)+log((1/2)^4.5bil) then divide by 1.8 to get the t alone?

Use the rules above to get a formula
a = b + c * t
and solve for t.