The bacterium Streptococcus pyogenes (S. pyogenes) is the cause of many human diseases, the most common being strep throat. The doubling time of these bacteria is 30 minutes, but in the presence of a certain antibiotic the doubling time is 6 hours. Two cultures are prepared, and the antibiotic is added to one of the cultures. Initially, each culture has 200 bacteria. (a) Find an exponential model for the number of S. pyogenes bacteria in each culture after t hours. fno antibiotic(t) = bacteria fwith antibiotic(t) = bacteria

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.