We put 2 flasks inoculated with Bacillus cereus in 37⁰C: one with 100μg/ml penicillin + 50μg/ml chloramphenicol and the other without penicillin. We found that the OD is higher in the one without the penicillin. These strains are supposedly penicillin resistant as verified by growing them in a test-tube containing penicillin (5mg/ml) at 30⁰C. It contradicts my hypothesis that they should have the same growth rate because of the $\beta$-lactamase secretion that would destroy the penicillin. I can't find any explanation in the web. help me
Your hypothesis is incorrect.
You must be assuming that lactamase destroys the antibiotic with perfect efficiency. This is incorrect.
You must be assuming that the population will remain genetically stable. This is doubly incorrect. Firstly the penicillin will select highly resistant bacteria which suffer a greater fitness burden from expressing the lactamase. Second, in absence of penicillin, spontaneously arising mutants which suppress the lactamase are free to proliferate.
You must be assuming that carrying capacity is identical for Pen+ and Pen- media. Trivially, you claim your experiment disproves this, but the assumption is also baseless since this need not be the case.
Furthermore, your results are inconclusive. You lack crucial controls, such as putting the bacteria from the Pen+ into Pen- and vice versa to see if the growth difference is intrinsic. You have not only failed to provide the error of your measurements, but have failed to provide the quantitative measurements themselves, so we do not even know if the difference is statistically significant.
Lastly, there are several basic things which you could rightfully expect us to assume, but have nevertheless failed to provide. For instance, you do not say if the populations are clonal.