Determine the point of inflection of p(t) = 20/(1 + 3e^-0.02t).

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beckden | High School Teacher | (Level 1) Educator

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The point of inflection is when a curve changes concavity.  This equates to the second derivative being zero at points of inflections.

We can use the chaing rule that `(d)/(dx)1/u = -1/u^2(du)/(dx)`


` = -20/(1+3e^(-0.02t))^2(3(-0.02)e^(-0.02t))=(1.2e^(-0.02t))/(1+3e^(-0.02t))^2`




This can be zero when `(-1+3e^(-0.02t)) = 0`

We get `3e^(-0.02t)=1`



`t = (-ln(3))/(-0.02)=50ln(3)~~54.93` This is the point of inflection.

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