Need help with chem calculations?

Question

I got 99 for the first
93 for the second and 33 for the third. The first one was marked correct but the otehrs wrong. Please help

The half-life of 241Am is 432.2 years. What percentage of a 241Am sample remains after 58 days?
% 99
What percentage of sample remains after 58 years?
%
What percentage of sample remains after 580 years?
%

Answer 1

The amount of sample remaining may be expressed as:
m = m(i) * 1/2^(t/λ), where m(i) is the initial mass, and t is the time elapsed, and λ is the half life.

For the percentage, you just take 1/2^(t/λ),

In short, you're taking the exponent of 1/2 to the fraction of how many half-lives have elapsed.

1.) 58 days is 0.1589 year.
1/2^(.1589/432.2) = 0.9998 = 99.98% of the sample.

2.) 1/2^(58/432.2) = 0.9112 = 91.12% of the sample.

3.) 1/2^(580/432.2) = 0.3945 = 39.45% of the sample.