How can I write an equation with superscripts using annotate in ggplot2?

I am having trouble figuring out how to write out an equation using annotate in ggplot2.

Here is an example of what I want to get, I just can't figure out how to get the superscripts in the equation and R^2 there.

Here is the code I have so far:

df4 <- data.frame(hours=c(0,1,3,5,12,24,48,96,168,336,504,720), copies=c(603.3,406,588,393.27,458.47,501.67,767.53,444.13,340.6,298.47,61.42,51.6))
p1 <- ggplot(df4, aes(x=hours, y=copies)) + geom_point() + stat_smooth(method = 'nls', method.args = list(start = c(a=543.4172,b=-0.00247)), formula = y~a*exp(b*x), se=FALSE, linetype=2, colour="pink") + theme_classic() + xlab("") + ylab("") + 
  annotate("text", x = 400, y = 750, label = "N(t)=543.4172e^-0.00247259t\nR^2 = 0.6933", color = "black", hjust = 0,  vjust = 1) +
  ggtitle(expression("eDNA pH 4"))
p1

I've been looking at other posts but just can't seem to get it to work.

Thanks in advance for any help or advice!

Solution

Another option would be to use parse=TRUE in annotate. Additionally your label requires some fixes to make it a valid expression. See ?plotmath.

Note, TBMK you can't have any line breaks in math expressions. For that reason I added the two lines of your label via two annotates where I have set vjust so that they are plotted on top of each other:

df4 <- data.frame(hours = c(0, 1, 3, 5, 12, 24, 48, 96, 168, 336, 504, 720), copies = c(603.3, 406, 588, 393.27, 458.47, 501.67, 767.53, 444.13, 340.6, 298.47, 61.42, 51.6))

library(ggplot2)

p1 <- ggplot(df4, aes(x = hours, y = copies)) +
  geom_point() +
  stat_smooth(
    method = "nls", method.args = list(start = c(a = 543.4172, b = -0.00247)), formula = y ~ a * exp(b * x),
    se = FALSE, linetype = 2, colour = "pink"
  ) +
  theme_classic() +
  xlab("") +
  ylab("") +
  annotate("text",
    x = 400, y = 750, label = "K(t) == 543.4172^{-0.00247259*t}",
    parse = TRUE,
    color = "black", hjust = 0, vjust = -.1
  ) +
  annotate("text",
    x = 400, y = 750, label = "R^2 == 0.6933",
    parse = TRUE,
    color = "black", hjust = 0, vjust = 1.1
  ) +
  ggtitle(expression("eDNA pH 4"))
p1