If you have 10,000 grams of a substance that decays with a half-life of 14 days, then how much will you have after 70 days?

Question

Show your work and round your answer to the nearest whole number.

Answer 1

After 1 half-life (14 days), the amount of substance remaining is half of the original amount:

10,000 grams / 2 = 5,000 grams

After 2 half-lives (28 days), the amount remaining is half of the amount remaining after 1 half-life:

5,000 grams / 2 = 2,500 grams

After 3 half-lives (42 days), the amount remaining is half of the amount remaining after 2 half-lives:

2,500 grams / 2 = 1,250 grams

After 4 half-lives (56 days), the amount remaining is half of the amount remaining after 3 half-lives:

1,250 grams / 2 = 625 grams

After 5 half-lives (70 days), the amount remaining is half of the amount remaining after 4 half-lives:

625 grams / 2 = 312.5 grams

Rounding to the nearest whole number, you would have approximately 313 grams remaining after 70 days.

Answer 2

or, done in a more direct way:

amount = 10,000(1/2)^(70/14)
= 10000(1/2)^5
= 10000(1/32) = appr 313

Answer 3

Yes, that is another way to calculate it directly using the formula A = A0(1/2)^(t/T), where A0 is the initial amount, t is the time elapsed, and T is the half-life. This formula gives the same result as the step-by-step approach.