An epidemic follows dIdt=0.1I(1−I500)\frac{dI}{dt} = 0.1I(1 - \frac{I}{500})dtdI=0.1I(1−500I). If I(0)=50I(0) = 50I(0)=50, what is I(t)I(t)I(t)?
I(t)=5001+9e−0.1tI(t) = \frac{500}{1 + 9e^{-0.1t}}I(t)=1+9e−0.1t500
I(t)=5001+e−0.1tI(t) = \frac{500}{1 + e^{-0.1t}}I(t)=1+e−0.1t500
I(t)=50e0.1tI(t) = 50e^{0.1t}I(t)=50e0.1t
I(t)=500(1−e−0.1t)I(t) = 500(1 - e^{-0.1t})I(t)=500(1−e−0.1t)