### Home > CAAC > Chapter 13 > Lesson 13.OF2-S > Problem 7-146

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?

How long will it take to reduce to 1% of the original amount?

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

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)* ^{x}*. Substitute 10 for

*x*.

Use the equation below, where *x* is the number of years.

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

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

≈ 6600 years