Question

Need help with the attached (rounded to the nearest hundredth)

Answer 1

We will have the following:

a)

`\begin{gathered} A(10)=700^(-0.031(10))\Rightarrow A(10)=513.4128694... \\ \\ \Rightarrow A(10)\approx513.41 \end{gathered}`

So, after 10 years the sample left will be approximately 513.42 g.

b) We determine the time it will take to get half the sample, that is:

`\begin{gathered} 350=700e^(-0.031t)\Rightarrow(1)/(2)=e^(-0.031t)\Rightarrow ln(2)=-0.031t \\ \\ \Rightarrow t=(ln(2))/(0.031)\Rightarrow t=22.35958647... \\ \\ \Rightarrow t\approx22.40 \end{gathered}`

So, it will take approximately 22.40 years.