df <- read.table('/home/edisz/Downloads/so/QueryResults.csv', sep = ',', 
                 header = TRUE)
df$date <- with(df, as.Date(paste(Year, Month, Day, sep = '-')))
df <- df[order(df$date), ]
df$csum <- cumsum(df$Total)
plot(csum ~ date, data = df, type = 'l', ylim = c(0, 100000))
abline(h = 100000, lty = 'dotted')

# numeric date
df$time <- as.numeric(df$date) / 100
takedf <- df[df$Year >= 2015, ]
require(mgcv)
m1 <- gamm(csum ~ s(time, bs = 'ps', k = 30), data = takedf)

# predict data
pdat <- data.frame(time = seq(min(takedf$time), 167, 0.01))
pdat$date <- as.Date(pdat$time * 100, origin = '1970-01-01')
pdat$pred1 <- predict(m1$gam, newdata = pdat)
pdat[pdat$pred1 > 100000, "date"][1]
## [1] "2015-07-22"

Based on this model, SO [r] tag will hit the 100.000 questions on 22.07.2015.

plot(csum ~ date, data = takedf, type = 'l', ylim = c(0, 100000), 
     xlim = range(pdat$date), main = '2015')
abline(h = 100000, lty = 'dotted')
lines(pdat$date, pdat$pred1, col = 'red')
abline(v = pdat[pdat$pred1 > 100000, "date"][1], lty = 'dotted')

# add insert of whole time series
u <- par("usr")
v <- c(
  grconvertX(u[1:2], "user", "ndc"),
  grconvertY(u[3:4], "user", "ndc")
)
v <- c(v[1] + 0.1,
       (v[1] + v[2]) / 2 , 
       v[3] + 0.1,
       (v[3] + v[4]) / 2)
par(fig = v, new = TRUE, mar = c(0,0,0,0) )
plot(csum ~ date, data = df, type = 'l', ylim = c(0, 100000), lwd = 2)
abline(h = 100000, lty = 'dotted')
lines(pdat$date, pdat$pred1, col = 'red', lwd = 2)