# Math

posted by .

The half-life of radioactive strontium-90 is approximately 32 years. In 1961, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it take until only 8 percent of the original amount absorbed remains?

• Math -

Since 1/8 = (1/2)^3, it will take 3 half-lives, or 96 years.

• Math -

I would say
.08 = (1/2)^(t/32)
ln .08 = (t/32) ln .5
t/32 = ln .08/ln .5 = 3.6438..
t = 116.6 years

rough check:
after 32 years --- 50% left
after 64 years --- 25% left
after 96 years --- 12.5% left , (which is 1/8 but not 8%)
after about 16 more years we would lose about 1/4 of what was left, leaving appr 3/4 of 12.5 or appr 9%

• math - oops -

ouch. How did I read 8% as 1/8?

As usual, go with Reiny's answer!

## Similar Questions

1. ### Calculus

[Exponential growth & decay] The half-life of radioactive strontium-90 is approximately 29 years. In 1965, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's …
2. ### Calculas

In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 32 years, what fraction of the strontium-90 …
3. ### Calculus

The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it …
4. ### AP Environmental Science (URGENT)

Strontium-90 is a radioactive waste product from nuclear reactors. It has a half-life of 29 years. How many years will it take for a quantity of strontium-90 to decay to 1/16 (one-sixteenth) of its original mass?
5. ### calculus

In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear weapons and got into the bones of people alive at the time. If the half-life of strontium-90 is 27 years, what fraction of the strontium-90 …
6. ### Math

The half-life of radioactive strontium-90 is approximately 28 years. In 1962, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it …
7. ### Calculus

The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's bones. How many years does it …
8. ### chem

Radioactive substances decay by first-order kinetics. How many years would be required for a sample containing strontium-90 to decrease to 58.32% of its initial activity?
9. ### Forensics

Strontium-90 is a radioactive waste product from nuclear reactors. It has a half life of 29 years. How many years would it take for a quantity of strontium-90 to decay 1/16 of its original mass?
10. ### Math

The element strontium-90 is radioactive. The percent of strontium -90, A(t), left in a sample can be modelled by the half-life function A(t) = A0 (1/2)^t/29, where t represents the time, in years, after the initial time, and A0 represents …

More Similar Questions