# A radioactive substance follows the equation N=N_0 e^-kt. It has a half life of 10 days. If initially, you...have 100 grams. How much will remain after 30 days. (assume e=2.718) Show complete...

A radioactive substance follows the equation N=N_0 e^-kt. It has a half life of 10 days. If initially, you

...have 100 grams. How much will remain after 30 days. (assume e=2.718)

Show complete solution and use checking in the answer

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`N = N_0 e^(-kt)`

If the substance has a half life of 10 days,

`N/(N_0) = e^(-kt)`

`1/2 = e^(-k xx 10)`

Taking logarithm,

`ln 0.5 = -k xx 10`

`k = 0.6931/10`

`k = 0.06931`

If intially you have 100 grams, after 30 days you would have,

`N = 100 xx e^(-0.06931 xx 30)`

N = 12.5 grams.

Therefore, there would be 12.5 grams left after 30 days.

Actually you dont need to solve any equation for this. If the half life is 10 days, then after first 10 days you would have only 50 grams and after second 10 days it would be reduced to 25 grams. Finally after 3rd 10 days, you would have 12.5 grams.