Question 469358
General exponential function:
{{{P(t) = P*e^kt}}}
where P is initial value, t is time, k is constant
For this problem we know P and t
P = 474
t = 9
However, k is unknown, but they tell us that when t=66, P(t) = P/2
Half-life just means you have half what you started with 
Using this we can solve for k:
{{{474/2 = 474*e^(66k)}}}
Divide by 474 on both sides
{{{1/2 = e^(66k)}}}
Take natural log of both sides: ln(e^a) = a
{{{ln(1/2) = 66k}}}
Divide by 66 on both sides
{{{(ln(1/2))/66 = k}}}
Use scientific calculator to approximate
{{{k = -.0105}}}
Now substitute this in for k in general equation to solve for P(9)
{{{P(9) = 474*e^(-.0105*9)}}}
{{{P(9) = 431.25}}}