# Math Help - Bacterial Cultures

1. ## 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

2. 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...