Question

radium has a hlaf life of 1620 years,. what % of the original amount of the radium sample would remain after 1000 years?
Halp;... 1/2P=Pe^kt isnt working for me..

Answer 1

Show me your work so far...

Answer 2

that way I don't start explaining it the other way and confuse you unnecessarily...

Answer 3

Just start frm the begininng. i dont know what im doing.

Answer 4

1/2P=Pe^kt

half the initial amount = initial amount * decay rate e^kt

Answer 5

the P, initial amount can be cancelled

\[\huge \frac{ 1}{ 2 }=e^{k*t _{1/2} }\]

Answer 6

but why is t/2?

Answer 7

they give you the point for the half life , when t=1620, solve for the constant k

Answer 8

then you have a general formula

y = P*e^{k*t}

for the amount left y, after t years

Answer 9

\[P(t) = P_0 (\frac{1}{2})^{t/t_{\text{half}}}\]is how I like to figure it out

\(P_0\) is the initial amount. \(t_{\text{half}}\) is the half-life

\[P(1000) = P_0(\frac{1}{2})^{(1000/1620)} = P_0(0.651897)\]
That means you have approximately 65.2% of the initial amount remaining after 1000 years.

Answer 10

y/P is the fraction percent they want

Answer 11

The exponential form is very useful, but I think it is a little easier for people new to the material to see how it works with a power of 1/2 instead of a power of e...

Answer 12

Ahh i see!!!! The E is fine :p

THANK YoU!

Answer 13

right on, both are good