Posted by **Z32** on Tuesday, October 6, 2009 at 8:08pm.

[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 bones. How many years does it take until only 14 percent of the original amount absorbed remains?

time= ____ years

- Calculus -
**Reiny**, Tuesday, October 6, 2009 at 8:25pm
Many math-teachers use base e for most exponential problems of this type, but since "half-life" is involved, let's use 1/2 as the base

amount = a(1/2)^(t/k) or

amount = a(2)^(-t/k) where a is the initial amount, t is the time in years, and k will be 29

so we have to solve

.14 = 1(2)^(-t/29(

take the ln of both sides

ln .14 = -t/29(ln 2), hope you know your log rules

-t/29 = ln .14/ln 2

-t/29 = -2.8365

t = 82.26 years.

check: after 29 years, we have 50% left

after 58 years we have 25% left

after 87 years we would have 12.5% left.

our answer appears reasonable.

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