1. Iron Man and His
Radioactive
Gaseous
Substances!
By flickr user chanchan222

2. Breaking Into Iron Man’s
Home; The Question…
Thanks to B’s lack of coordination Iron Man’s
house was filled with 410g of a radioactive gas
that, when too much is inhaled, will prove
DEADLY! We have discovered that a safe amount of
gas to be around is 25mg.
1. How long will we have to wait to get back into the
house if the substance’s half life is 0.6 hours?
a) Find the decay constant
b) Find out how long it will take for the gas to
disperse to a safe level.

3. Make sure everything
is in the same unit!
Uh oh! We need to change 410g
into mg or else we’ll get the
wrong answer!
410g x = 410000 mg
That means it is definitely not safe to enter! Now
we have to use some other math tricks to find out
when it will be safe to return…

4. Let’s use this formula to
help us figure out when it
will be safe to return to
Iron man’s house!
A= Pert
A is the amount at the end of the term.
P is the initial amount.
r is the growth or decay constant.
t is time in hours.

5. Let’s write down what
we know!
P= 410000 mg
Safe amount= 25mg
r=?
t=?
Oh no! We don’t have r or t
what are we going
to do?!?!

6. WHAT ARE WE GOING
TO DO ?! D:
Well! let’s try finding the decay constant (r)
We know that half-life means the substance will
decrease it’s size by half every x amount of
hours. Hmm… let’s try plugging this into the
equation to find the decay constant!
410000 ÷ 2= 205000

7. Finding the decay
constant
1. Plug in our numbers
205000= 410000er (0.6)
0.5= er(0.6) 2. Divide both sides by 410000.
3. Change it into a logarithm.
ln(0.5) =r(0.6) REMEMBER A LOGARITHM IS AN
EXPONENT logbc=a.
4 Since e is special, it is called the
= natural logarithm. So instead of log
we write ln (but don’t write e as the
base).
=r 5. Divide both side by 0.6
6. Keep the exact value since our
answer is just a decimal
r = -1.1552 approximation.

8. Let’s Plug It In ;)
A = Pert
25 = 410000e( )(t) 1. Plug in our numbers.
6.0976 x 10-5 = e( )(t) 2.
3.
Divide both sides by 410 000.
Remember a logarithm is an
exponent. Treat this as you would
ln6.0976 x 10-5 = (t) treat a logarithm but write ln
instead of log.
-9.7050 = (t) 4. Solve for ln 6.0976 x 10 -5
(-9.7050) = (t) 5. Divide both sides by or
multiply by the reciprocal.
t = 8.4008
6. This is your answer in hours.
That is approximately 8.4 hours.

9. Now that we know when it will
be safe to enter the house…
It’s time for a lunch
break!
:D