RELAZIONI E FUNZIONI PRACTICE WITH CLIL The recovery time Laboratory studies have shown that the wound healing process can be described through an exponential model. If we indicate with S the area, in mm2 of the surface, this varies, as a function of time (in days) according to the law: S(t) = S 0 e 0.35t where S0 is the area of the surface initially affected by the wound and e is an irrational number called Napier s constant, which we will have the opportunity to talk about in the next unit and is approximately 2.718. Let us calculate If the wound surface measures 100 mm2, how long will it take for it to be reduced by half? If S0 = 100 mm2 we want to calculate the value of t at which S(t) = 50 mm2 and then solve the equation: 50 = 100 e 0.35t e 0.35t = 0.5 In a graph, we represent the function: y = e 0.35t and the line: y = 0.5 y 2 1,5 1 0,5 A O 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 x The two functions intersect at point A of abscissa 1.98 so the wound will have reduced to 50% after 2 days. And answer 1. Does it make sense to study the trend of the function also in the 2nd quadrant of the Cartesian plane? Motivate your answer. 2. According to this model, how long will it take for the wound to heal completely? 264

PRACTICE WITH CLIL