The percent remaining after n half-lives is calculated using which expression?

The percent remaining after n half-lives is calculated using which expression?

• A. n/2
• B. (1/3)^n
• C. 1/2^n
• D. e^(-n)

Answer: (C)

Each half-life reduces the amount to half of what it was. After n of these steps, the remaining portion is (1/2)^n, which is the same as 1/2^n. This is the geometric decay pattern that occurs with discrete halving. The other forms don’t match this halving process: linear n/2 would not account for repeated halving, (1/3)^n would imply cutting to a third each time, and e^(-n) describes continuous exponential decay rather than discrete half-lives. So the correct expression for the remaining fraction is 1/2^n. If you want the percent, multiply by 100.

Each half-life reduces the amount to half of what it was. After n of these steps, the remaining portion is (1/2)^n, which is the same as 1/2^n. This is the geometric decay pattern that occurs with discrete halving. The other forms don’t match this halving process: linear n/2 would not account for repeated halving, (1/3)^n would imply cutting to a third each time, and e^(-n) describes continuous exponential decay rather than discrete half-lives. So the correct expression for the remaining fraction is 1/2^n. If you want the percent, multiply by 100.