An unknown radioactive element decays into non-radioactive substances. In 480 days the radioactivity of a sample decreases by 35 percent.

Question

A) What is the half-life of the element? 

B) How long will it take for a sample of 100mg to decay to 76mg?

Answer 1

a)

0.65 = e^480k

ln 0.65 = 480k

-0.43 ≈ 480k

-0.000897 ≈ k

0.5 = e^-0.000897t

ln 0.5 = -0.000897t

-0.693 ≈ -0.000897

772.7 ≈ t

b)

76 = 100(0.5)^{772.7 / t}

Can you solve for t and answer?