You have found a mysterious substance that appears to be radioactive. You take a sample to a nuclear chemist who measures out 100 g. of the substance. Thirty hours later, the chemist tests the sample and finds that 6.25 grams of the sample remains radioactive. What is the half-life of the sample?
a. 4 hours
b. 7.5 hours
c. 15 hours
d. 30 hours
*not d*

Question

You have found a mysterious substance that appears to be radioactive. You take a sample to a nuclear chemist who measures out 100 g. of the substance. Thirty hours later, the chemist tests the sample and finds that 6.25 grams of the sample remains radioactive. What is the half-life of the sample?
a. 4 hours
b. 7.5 hours
c. 15 hours
d. 30 hours 
*not d*

matt101 · Answer

The general equation for half-life decay is:

$$m=m_0\left( 1 \over 2 \right)^{t \over t_{0.5}}$$
Where m is the final mass, m(0) is the initial mass, t is the total time elapsed, and t(0.5) is the length of the half-life.

You're given all the information in the question but the half-life itself, so just solve for t(0.5) and you'll have your answer!