## anonymous 4 years ago An isotope has a half-life of 5,000 years, How long will it take to decay to 15% of its original quantity?

1. anonymous

$f(t) = Ae ^{kt}$$k = \frac {-ln 2}{t _{\frac{1}{2}}} = \frac {-ln 2}{5000} = 0.000138629436$We'll let A = 100, so its easy to see the percent change.$f(t) = 100e^{0.000138629436t} = 15$$.15 = e^{-0.000138629436t}$$t = \frac {\ln .15}{-0.000138629436} \approx 13685 years$

2. anonymous

The constant is negative in the exponential decay equation, I made a mistake when I first wrote the equation. $f(t) = Ae^{-kt}$

3. anonymous

okay thank you. may i ask though how you found k?

4. anonymous

Exponential decay is first order, so there is a formula that relates the half life and the constant.$t _{\frac{1}{2}}^{} = \frac {-\ln 2}{k}$

5. anonymous

okay, thank you very much!

6. anonymous

Alright, no problem, good luck with your studies :)