please show steps. A small town has 4000 inhabitants. At 8 AM, 320 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor? (Round the answer to one decimal place.

Question

Use this equation to solve, y=yo/((1-yo)e^-kt +yo)

Answer 1

I don't see any differential equation. This is just logistical growth. And, you left out a scale factor. The general equation is

y = (Ly₀)/(y₀+(L-y₀)e^(-kt))
Now just plug in your y₀ and you get

y = 4000L/(4000+(L-4000)e^(-kt))
Now just plug in your given points:
4000L/(4000+(L-4000)e^(-8k)) = 320
4000L/(4000+(L-4000)e^(-12k)) = 2000

a quick google search will provide you with the actual differential equation.