log applications - half life

[a_vanderbrook]

I have no idea how to solve this problem: help or hints would be great.
The directions state: find the missing parts of the given radioactive isotope (226 Ra) using this equation... Q(t)= Ce^kt

where Q(t) is the quantity at any time
where C is the starting amount
where K is the constant rate of decay
and where t is the time

The following information is provided:

half- life (years) = 1620
... I know this is the time, "t"

initial quantity = 10 g
... I know this is the starting amount, "C"

e = constant

So the question is how will I find both the Q(t) and the k?

Thanks so much!

 

[stapel]

I have no idea how to solve this problem....

The first step in this sort of exercise is to use the half-life information to find the decay constant "k". With the values plugged in for "C" and "k", you would then have your function Q. The customary next step would be to use Q in some way, but I don't see that this sort of question is included...?

The only way to solve for "k", however, is to use logarithms. Since you have "no idea" how to do this, then you will need to do a lot of self-study to get caught up. (We cannot provide the missing classroom instruction. Sorry.)

You might want first to study up on logs, log rules, exponentials, solving log equations, and solving exponential equations, before proceeding any further. Once you have studied one or a few lessons on each of these topics, you will then be prepared to tackle this exercise.

The material isn't "way hard", but do allow yourself a few days to absorb the concepts.

Eliz.

Note: The above assumes that you are familiar with variables, functions, function notation, solving linear equations, and solving literal equations.

 

[a_vanderbrook]

i know the basics of doing concepts like this, but the only thing that is confusing is how do i find k when there are two unknown variables, k and q(t)

 

[a_vanderbrook]

nevermind, i figured this problem out on my own.
thanks any way.

 

[stapel]

how do i find k when there are two unknown variables, k and q(t)

Q(t) is not an "unknown variable". It is the name of the function, "Q as a function of t". (So you might want to brush up on functions and function notation.)

To find the value of the constant (not "variable") "k", you would need to follow the instructions provided earlier: Plug in the values of Q, C, and t for the half-life, and solve (using logs) for the (fixed) value of k. (So you might want to brush up on variables, logs, and how to solve exponential equations.)

Thank you.

Eliz.