How to create a proportional buffer based on population of a different shape's field? (Equity Mapping)

[GabePreston]

I am trying to create an "equity map" that shows proximity of different types of parks and facilities to a determined population of a town.

(ex. neighborhood parks to nearest 500 people, and create a buffer or ring of sorts to those 500 people surrounding the parks)

I have a census file of all blocks within the town and was able to tie in block population data, so each block within the town has a population number. I also have created all the shapefiles for parks / facilities / fairgrounds, etc.

I don't know how to create a proportional buffer around the input features (parks) to the determined population (from block groups surrounding those parks). In theory the map would look something like the photo attached, but on a finer scale... 

Has anyone made a map like this, or know how to run this function? I am using ArcMap 10.5 and would love any and all input on how to create these specified buffers.  

Thank you! 

[DanPatterson_Retired]

like a buffer by field value http://pro.arcgis.com/en/pro-app/tool-reference/analysis/buffer.htm

what is in your table that you could use?

[AdrianaAbramovich2]

what about finding the service area per park based on a 20 minutes walk from each park? then find gaps of service. 

To come up with the number of people in the area of service, find how many units per block by housing category. 

For single family, multiply by 2.5, for multifamily use 2.32.  the intersect of the area of service and the total population will give you an idea a number of total population served by those parks. if you calculate maximum growth based on zoning designation, you will get a number of the projected number based on density.