Logistic curve / sigmoidal curve

[mcdonald60]

I have numbers corresponding to years 2015(1.5), 2030(6), and 2050(10.5). I want to make a projection for the years in between in 5 year segments (2015,2020,2025,2030,2035,2040,2045,2050) that yields logistic growth, or a sigmoidal curve, when plotted on a line graph. Can anyone tell me the equation to figure out the numbers in between these given data points?

Thank you