Exponential Decay

chrozer · #1 $Old$ November 30th, 2008, 05:18 PM

Quote:

A lab culture initially contains 500 bacteria. Two hours later, the number of bacteria has decreased to 200. Find the exponential decay model of the form
$B=B_0a^{kt}$
that can be used to approximate the number of bacteria after $t$ hours.

I have no idea where to start. Any ideas?

skeeter · #2 $Old$ November 30th, 2008, 06:19 PM

$B_0$ is the initial population at $t = 0$ ... which is 500.

you were given another point on the curve , $(2,200)$

so, sub in 200 for B and 2 for t ... solve for k.

chrozer · #3 $Old$ November 30th, 2008, 07:52 PM

Quote:

Originally Posted by skeeter $View Post$

$B_0$ is the initial population at $t = 0$ ... which is 500.

you were given another point on the curve , $(2,200)$

so, sub in 200 for B and 2 for t ... solve for k.

What would you sub in for a though?

Cause when I substitute what you said, I get the equation $200 = 500a^{2k}$ and when I solve for $k$ , I get $k = \frac {log_a\frac{2}{5}}{2}$ . What would a be?

skeeter · #4 $Old$ December 1st, 2008, 05:49 PM

"a" can be any positive value you want that doesn't equal 1.

I'd use "e" since it's calculator friendly.

chrozer · #5 $Old$ December 1st, 2008, 05:52 PM

Quote:

Originally Posted by skeeter $View Post$

"a" can be any positive value you want that doesn't equal 1.

I'd use "e" since it's calculator friendly.

Ok thanks alot. I finally got it.