Question

the half life of a certain radio active material is 42 hours. an initial amount of the material has a mass of 292 kg. write an expononetial function that models the decay of the material. Find how much radioactive material remains after 11 hours.

Answer 1

are you aware of the formula to find the decay constant of a radioactive sample?

Answer 2

as well as the value of the decay constant with respect to half life

Answer 3

First, find the decay constant\[\frac{A_0}{2}=A_0e^{42k}\implies \frac{-\ln(2)}{42}=k \approx -0.0165\]

Answer 4

Given that, you are in business. The form of the function is\[A(t)=A_0e^{kt}\]With the information we just calculated and the facts from the problem,\[A(t)=292e^{0.0165t}\]