In 10 years, 25% of a radioactive substance decays. What is its half-life?

A. 25 years
B. 24 years
C. 20 years
D. 29 years

(1/2)^(10/x) = .75

x = 24

You first have to find your rate

.75 = e^ (r)(10)

Then find the time for half- life

.5 = e^ (r from above)(t)

Thanks

24 To determine the half-life of a radioactive substance, we need to calculate the amount of time it takes for half of the substance to decay. In this case, since we know that in 10 years 25% of the substance decays, we can find the half-life by determining how many 10-year periods it takes for the substance to decay by 50%.

Let's break it down step by step:

1. Start with the initial amount of the substance (100%): 100%
2. After 10 years, 25% has decayed: 100% - 25% = 75%
3. After another 10 years (20 years total), another 25% decays: 75% - 25% = 50%

Therefore, it takes 20 years for the substance to decay by 50%, which means the half-life is 20 years.

The correct answer is C. 20 years.