I am trying to find point where the slop of my data changes significantly. I want to determine a single point (in this case a value for days) in order to use it as an argument in model I try to run.

study_data <- data.frame(days = c(30,50,100,133,166,200,233,266,300,333,366,400,450,500,750) ,
                 participants = c(100,85,60,45,36,30,27,23,21,19,19,17,16,16,6))

plot(df$days, study_data$participants)

using the cpop package gave me multiple points of change.

cpop plot

I wasn’t able to get the segmented package to run, and I am not sure if it is even appropriate for my data. Are there any good ways to approach this?