Question 270807
The following table shows the amount of polonium in milligrams remaining after x days from an original sample of 2 milligrams.
x(days) 0 100 200 300
y milligrams 2 1.22 0.743 0.453
:
a. is the half life of the polonium less than 200 days?
Find the half life (h) using values for 100 days and resulting amt of 1.22 mg
2*(2^(-100/h)) = 1.22
:
2^(-100/h) = {{{1.22/2}}}
;
2^(-100/h) = .61
:
log(2^(-100/h)) = log(.61)
{{{-100/h}}}log(2) = log(.61)
{{{-100/h}}}= {{{log(.61)/log(2)}}}
{{{-100/h}}} = -.713
h = {{{100/.713}}}
h ~ 140 days is the half life
:
b. give a general formula that can be used to approximate the amount A of polonium after x days.
A = 2*2^(-x/140)
:
:
c. what is the half-life of the polonium?
we found it to be 140 days in (a)
:
 GRaph A(x) and show th epoint that would show the half-life for x=2 milligrams.
Graph the equation y = 2*2^(-x/140)
{{{ graph( 300, 200, -50, 325, -1, 3, 2*2^(-x/140)) }}}
You can see that at 140 days there is about 1 mg of the substance