Question

The half-life of silicon-32 is 710 years. If 100 grams is present now,how much will be present in 300 years? (Round k-value to six decimalplaces and round your final answer to one decimal place) y= nekkt

Answer 1

We will have the following:

`N=Noe^(kt)`
`50=100e^(710k)\Rightarrow0.5=e^(710k)\Rightarrow\ln (0.5)=710k\Rightarrow k=(\ln(0.5))/(710)`

From this we have that the equation is:

`N=100e^{((\ln(0.5))/(710))t}`

Now, we replace the time:

`N=100e^{((\ln(0.5)/(710))(300)}\Rightarrow N\approx74.6`

So, there will be approximately 74.6 grams of silicon-32.