<PRE><B>Question 301757</B>
    A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value.
.
Use the exponential growth/decay formula:
{{{P(t) = Po*e^(rt)}}}
Where
P(t) is amount after t time
Po is the initial amount
r is the rate of growth/decay
t is time
.
Using the first sentence we can determine r:
(1/2)(200) = 200e^(r*20)
1/2 = e^(r*20)
ln(.5) = r*20
ln(.5)/20 = r
-.03466 = r
.
Our equation then is:
{{{P(t) = Po*e^(-.03466t)}}}
Now, we can answer:
How many cells of the bacteria will be left after 1 hour (60 minutes)? 
{{{P(t) = 200*e^(-.03466*60)}}}
{{{P(t) = 25 }}}
25 cells left after 60 minutes
</PRE>