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The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 6.2% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Round your answer to the nearest hundredth.

Respuesta :

Solution

for this case we have the following equation:

[tex]A=A_oe^{kt}_{}[/tex]

the constant would be:

k= -0.062

Then we can do this:

[tex]\frac{1}{2}A_o=A_oe^{-0.062t}[/tex]

solving for t we have:

[tex]\ln (\frac{1}{2})=-0.062t[/tex][tex]t=-\frac{\ln (0.5)}{-0.062}=11.179\text{days}[/tex]

Rounded to the nearest hundredth would be:

11.18 days

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