Question

Assuming a half life of 1599 years, how many years will be needed for the decay of 15/16 of a given amount of radium-226?

Answer 1

use the formula

\[m(t) = m_0 e^{-rt}\]

where,
t = time in years (it is your x value)
m(t) = the amount of material you have at time t in percent (it is your y value)
\[m_0 =\] the initial amount of material you have in percent
r = rate of decay

so from our question we know,
at
t = 1599
m(t) = 50%
\[m_0\] = 100%
because we are starting with 100% of material

so plug that into the formula

Answer 2

Once you plug it into the formula you have to solve for r, that way you can get a general equation to solve for the time (t) when there is 15/16 of the material left

Answer 3

Woah. Well... just for the record, my teacher hasn't taught us that formula. I'm just a sophomore. lol. He didn't teach it that way. I guess.. I'll try to do it that way though.

Answer 4

you can convert 15/16 to percent by multiply it by 100

Answer 5

He taught us to covert it into a decimal though. And that's the point where I don't know what to do.

Answer 6

yeah this is an equation you will see in grade 12 ha, yeah and you need to how to use logarithms to solve this problem but it is really easy and chances are you will see this equation again so smeh.

Here is a tutorial on how to convert fractions to decimals

http://www.mathsisfun.com/converting-fractions-decimals.html

Answer 7

Anyways if you plug all the stuff I provided into the formula you end up with

\[50 = 100e^{-r1599}\]

Now just solve for r

do you know how to solve for r? it only requires one logarithmic rule
That rule being:
\[\ln(e^x) = x\]

Answer 8

Someone the other day explained another method of solving these problems that may be easier for you.

If you want to check it out it is here:

http://openstudy.com/study#/updates/50a06c34e4b05517d5366777

Unless you are alright using the method I'm showing to you