Drug resistance to tuberculosis (TB) has become more widespread over the past decade. As such, understanding the emergence and fitness of antibiotic-resistant subpopulations is crucial for the development of new interventions. Here we use a simple mathematical model to explain the differences in the response to isoniazid (INH) of Mycobacterium tuberculosis cells cultured under two growth rates in a chemostat. We obtain posterior distributions of model parameters consistent with data using a Markov chain Monte Carlo (MCMC) method. We explore the dynamics of diverse INH-resistant subpopulations consistent with these data in a multi-population model. We find that the simple model captures the qualitative behaviour of the cultures under both dilution rates and also present testable predictions about how diversity is maintained in such cultures.