tabulka <- read.table (file = "population.txt", header = TRUE)

x <- tabulka$Year
Y <- tabulka$Population

Y1 <- Y / 0.3
Y2 <- log (1 + log (1 + log (Y1)))

model <- lm (Y2 ~ 1 + x + I(x^2))

model$coefficients

xx <- seq (0, 2000, by = 0.1)

YY <- 0.3 * exp (exp (exp (8.301576e-3 - 3.886778e-4 * xx + 4.035209e-7 * xx**2) -1) -1)

summary (tabulka)

plot (c (0, 2000), c (0, 6), type = "n", xlab = "rok", ylab = "populace")
points (x, Y, pch = 24, col = 4)
lines (xx, YY, col = 2, lwd = 1.5)