Question

A sample of a radioactive isotope had an initial mass of 610 mg in the 1990 and decays exponentially over time. A measurement in the year 1992 found that the sample's mass had decayed to 340 mg. What would be the expected mass of the sample in the year 1997, to the nearest whole number?

Answer 1

we get that the equation that models the situation is:

`m=610\cdot k^t^{}`

when t=2. We get that

`340=610\cdot k^2\rightarrow k=\sqrt[]{(340)/(610)}\approx0.75`

so we get that after 7 years ( 1997 )

`m=610\cdot(\sqrt[]{(340)/(610)})^7\approx79`