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The half-life of silicon-32 is 710 years. If 30 grams is present now, how much will be present in 300 years? Round answer to three decimal places. Using A(t)=A0e^(ln(0.5)/T)t

Respuesta :

Answer: 55.668 grams

General equation of exponential decay/growth:

N = Noe^(kt)

50 = 100e^(710k)

.5 = e^(710k)

ln(.5) = 710k

ln(.5)/710 = k

Therefore, our equation is now:

N = 100e^((ln(.5)/710)t)

Now, we substitute t with 600:

N = 100e^(ln(.5)/710)600

N = 100e^(-.585758)

N = 100(.556684)

N = 55.668 grams