# Bacterial Cultures

• May 21st 2007, 08:30 AM
mathnerd11
Bacterial Cultures
OK, another tricky question which I am having trouble with. We are given the equations for two bacterial cultures (which describe their rates of growth, y being equal to the number of bacteria at a certain time) Culture A has an equation of y = 50 (1.319507911)^x and Culture B has an equation of y = 65 (1.316074013)^x. The problem here is we are asked to find when the two cultures will be equal, and while i have done the necessary log calculations to determine this, I am left with an impossible answer (1.01 x = 1.3 x). If anybody could tell me what I'm doing wrong, it would be much appreciated! :)

Thanks so much!

mathnerd11 :)
• May 21st 2007, 11:58 AM
earboth
Quote:

Originally Posted by mathnerd11
OK, another tricky question which I am having trouble with. We are given the equations for two bacterial cultures (which describe their rates of growth, y being equal to the number of bacteria at a certain time) Culture A has an equation of y = 50 (1.319507911)^x and Culture B has an equation of y = 65 (1.316074013)^x. The problem here is we are asked to find when the two cultures will be equal, and while i have done the necessary log calculations to determine this, I am left with an impossible answer (1.01 x = 1.3 x). If anybody could tell me what I'm doing wrong, it would be much appreciated! :)

Thanks so much!

mathnerd11 :)

Hello,

I've got x is approximately 100.

And that's what I've done:

50 (1.319507911)^x = 65 (1.316074013)^x Divide both sides by 50 and by (1.316074013)^x
Code:

```  65        1.319507911 ---- = (-------------------)^x = 1.002609198^x  50        1.316074013```
I assume that you know how to calculate the value for x. My result: x = 100.6847...