A well-known study shows that the average person experiences a temporary drop in

Question

A well-known study shows that the average person experiences a temporary drop in IQ after watching "The Bachelor". Specifically, the stud showed that the rate at which the average person's IQ dropped was proportional to the difference between the person's IQ at a given time and a lower limit of 40. Suppose tha Mohamed, an average person with an IQ of 108, sits down to watch "The Bachelor". After 2 hours, an IQ test shows his IQ has dropped to 86. Give a differential equation and all initial conditions that model what is happenning to Mohamed's IQ as he is watching the show. Declare All variables and show how many hours Mohamed will have to watch to see his IQ drop to 70. Show all work Please :)

Explanation / Answer

let x = IQ

dx/dt = -k ( x - 40)

solve for x

x= A e^(-kt) + 40

we know t=0 x = 108

so A = 68

x = 68 e^(-kt) + 40

at t=2 x - 86

so

86 = 68e^(-k*2) + 40

k=0.19543

so x = 68e^(-0.19543*t)+40

70 = 68e^(-0.19543*t)+40

t=4.18 hours

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