Sally is sick with a bacterial infection so the doctor decid

Sally is sick with a bacterial infection, so the doctor decides to give her antibiotics The doctor starts Sally with a large initial dose that brings the concentration in her blood to 1 gram per liter He then puts her on a daily maintenance dosage that will raise the concentration by 0.3 grams per liter every night Suppose that Sally\'s body will use (or filter out) half of the medication in her blood stream daily. Find the equilibrium m* of the system with the given parameter values algebraically.

Solution

solution:

new concentration = old concentration - fraction used x old concentration +supplement

M_t+1 = M_t - 0.5 M_t +0.3

M_t+1 = 0.5M_t +0.3

The equillibrium point,

M^* = 0.5 M^* + 0.3

0.5 M^* = 0.3

M^* = 0.3/0.5

M^* = 0.6