I can't see how any of those formulas show exponential decay. (Did you type those correctly?)
The formula that will show the remaining amount correctly is:
ending amount = Bgng Amount / 2^n
where "n" is the number of haf-lives.
So, for example if half life = 4 hours and if we want to calculate the amount after 9 hours (that's 2.25 half-lives) then:
ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount = 50 / <span><span><span>4.75682846 </span>
</span></span><span><span>ending amount = </span> 10.5112 grams
</span>Looking at the graph, we see that's about right.
The formula that will show the remaining amount correctly is:
ending amount = Bgng Amount / 2^n
where "n" is the number of haf-lives.
So, for example if half life = 4 hours and if we want to calculate the amount after 9 hours (that's 2.25 half-lives) then:
ending amount = Bgng Amount / 2^n
ending amount = 50 / (2^(9/4))
ending amount = 50 / 2^2.25
ending amount = 50 / <span><span><span>4.75682846 </span>
</span></span><span><span>ending amount = </span> 10.5112 grams
</span>Looking at the graph, we see that's about right.