You take an initial sample from the water and estimate that there are million microbes in the pool. Assume that the bacteria grows according to a logistic growth model for population growth. Assume the carrying capacity is million microbes and the relative growth rate is k

$\mathrm{<font><font>(</font></font>}$a Determine the formula for the population of bacteria in the pool at time t measured in months. 

$\mathrm{<font><font></font></font>}$b You want to ensure that the bacteria population never exceeds  million. Determine when the bacteria population will reach  million to determine how often you should treat the water in the pool