Question

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.

Answer 1

for this case we have the following equation:

`A=A_oe^(kt)_{}`

the constant would be:

k= -0.062

Then we can do this:

`(1)/(2)A_o=A_oe^(-0.062t)`

solving for t we have:

`\ln ((1)/(2))=-0.062t`
`t=-(\ln (0.5))/(-0.062)=11.179\text{days}`

Rounded to the nearest hundredth would be:

11.18 days