How Not to Fit a Trend

If one of The Kids in Data Over Space and Time turned in something like this, I'd fail them ask where I'd gone wrong patiently talk them through all the reasons why blind, idiot curve-fitting is, in fact, idiotic, especially for extrapolating into the future. If they told me "well, I fit a cubic polynomial to the log of the series", we would go over why that is, still, blind, idiot curve-fitting.

library("covid19.analytics")
temp <- covid19.data("ts-deaths-US")

cu_deaths <- colSums(temp[,-(1:4)])
deaths <- c(0,diff(cu_deaths))
covid <- data.frame(cu_deaths,
                    deaths,
                    date=as.Date(names(cu_deaths)))
rownames(deaths) <- c()
plot(deaths ~ date, data=covid, type="l",
     lty="solid",
     ylim=c(0,3500),
     xlim=c(min(covid$date),
            as.Date("2020-08-04")),
     lwd=3)
start.date <- "2020-03-01"
working.data <- covid[covid$date>start.date,]
cubic <- lm(log(deaths) ~ poly(date, 3),
            data=working.data)
lines(x=working.data$date,
      y=exp(fitted(cubic)),
      col="red", lty="dashed", lwd=3)
future.dates <- seq(from=max(working.data$date),
                    to=as.Date("2020-08-04"),
                    by=1)
lines(x=future.dates,
      y=exp(predict(cubic,
                    newdata=data.frame(date=future.dates))),
      lty="dotted", col="pink", lwd=3)