Plutonium-210 has a half-life of 140 days. Use the formula, where, is the remaining mass, is the original mass, and is the half-life, to determine how long it takes to reduce 300 milligrams of plutonium-210 to 200 milligrams. Arrange the steps in the right order to solve the problem.

Since this is exponential decay we can express it as:

f=ir^t, f=final amount, r=common ratio, t=time

If the half life is 140 days we can say:

a/2=ar^140

.5=r^140

r=.5^ (1/140) now we can express our equation as:

f=i (.5^ (1/140)) ^t which is equal to:

f=i (.5) ^ (t/140) now we want to find the time necessary to reduce 300mg to 200mg so:

200=300 (.5) ^ (t/140) divide both sides by 300

2/3=.5^ (t/140) taking the natural log of both sides

ln (2/3) = (t/140) ln. 5 divide both sides by ln. 5

ln (2/3) / ln. 5=t/140 multiply both sides by 140

t=140ln (2/3) / ln. 5

t≈81.89 days (to the nearest hundredth of a day)