r - Plot intersecting curves

I want to create a simple plot displaying two intersecting curves like the one below:

(with an arrow indicating the intersection point)

I have been able to draw the intersecting curves with the following code:

I0 <- log(1)
b <- .1
d <- .014

curve(exp(I0 - b * x), 0, 50, col = "blue", lwd = 2)
curve(exp(d * x) - 1, 0, 50, add = TRUE, col = "red", lwd = 2)

But what I got is not a pair of "symmetrical" curves:

Any hints? (For this example I did not try to plot the arrow).

To find the point of intersection (your "d"), you can use uniroot.

f <- function(x) exp(I0 - b * x)
g <- function(x) exp(I0 - b * (30-x))
    
I0 <- log(1)
b <- 0.1

x <- uniroot(function(x) f(x) - g(x), interval=c(0,30))$root
y <- g(x)

curve(exp(I0 - b * x), 0, 30, col="blue", lwd=2)
curve(exp(I0 - b * (30-x)), 0, 30, col="red", lwd=2, add=TRUE)

y.axs <- par("usr")[3:4]
y0 <- y + diff(y.axs) / 10

arrows(x0=x, y0=y0, x1=x, y1=y, length = 0.15)
text(x=x, y=y0, expression(hat(S)), pos=3)