The equation will be of the form:
[tex]A(t)= A_{0} e^{rt}[/tex]
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
[tex]40=320e^{3r}[/tex]
Rearranging and taking natural logs of both sides, we get:
[tex]ln\ 0.125=3r[/tex]
[tex]r=\frac{ln\ 0.125}{3}=-0.693[/tex]
The required model is:
[tex]A=A _{0} e^{-0.693t}[/tex]
