### Home > CCA2 > Chapter 6 > Lesson 6.1.5 > Problem 6-77

The half-life of an isotope is 1000 years. A 50-gram sample of the isotope is sealed in a box. Homework Help ✎

How much is left after 10,000 years?

Half-life means time in which half of the original 50 grams will remain.

*y*=*ab*^{n}*a*is the initial value,*b*is the multiplier (0.5 since we are working with a half-life),*n*is the number of thousands of years, and

*y*is the amount of the isotope that remains (in grams).The equation is

*y*= 50(0.5). Substitute 10 for^{x}*x*.Use the equation below, where

*x*is the number of years.How long will it take to reduce to 1% of the original amount?

Use the equation from the help for part (a).

In this case,*y*= 1% of 50 and you are solving for*x*.≈ 6600 years

How long will it take until all of the original sample of the isotope is gone? Support your answer.