# Thread: Exponential Decay

1. ## Exponential Decay

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
$\displaystyle B=B_0a^{kt}$
that can be used to approximate the number of bacteria after $\displaystyle t$ hours.
I have no idea where to start. Any ideas?

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

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

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

3. Originally Posted by skeeter
$\displaystyle B_0$ is the initial population at $\displaystyle t = 0$ ... which is 500.

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

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 $\displaystyle 200 = 500a^{2k}$ and when I solve for $\displaystyle k$, I get $\displaystyle k = \frac {log_a\frac{2}{5}}{2}$. What would a be?

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

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

5. 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.

6. ## Re: Exponential Decay

Originally Posted by chrozer
Ok thanks alot. I finally got it.
What is the final answer? -.458?

7. ## Re: Exponential Decay

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

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### a lab culture initially contains 500 bacteria

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