Here's the formula for exponential decay:
[tex]A = p(1-k)^t[/tex]
(where A = new amount, p = principal (starting) amount, k = rate of decay, and t = time)
Let's use what we know and fill in the expression.
[tex]0.08 = 0.20(1-0.47)^t[/tex]
And now we solve for t.
[tex]0.08 = 0.20(0.53)^t \\ 0.4 = 0.53^t \\ log0.4=t*log0.53 \\ t = \frac{log0.4}{log0.53} = \boxed{1.44\ hours}[/tex]
