# Exponential Decay

• Nov 30th 2008, 03:18 PM
chrozer
Exponential Decay
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?
• Nov 30th 2008, 04:19 PM
skeeter
$B_0$ 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.
• Nov 30th 2008, 05:52 PM
chrozer
Quote:

Originally Posted by skeeter
$B_0$ 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?
• Dec 1st 2008, 03:49 PM
skeeter
"a" can be any positive value you want that doesn't equal 1.

I'd use "e" since it's calculator friendly.
• Dec 1st 2008, 03:52 PM
chrozer
Quote:

Originally Posted by skeeter
"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.
• Mar 6th 2013, 04:24 PM
Estelome
Re: Exponential Decay
Quote:

Originally Posted by chrozer
Ok thanks alot. I finally got it.

What is the final answer? -.458?
• Apr 15th 2013, 12:19 AM
ohiosuba
Re: Exponential Decay
I'd use "e" since it's calculator friendly.

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