model {
for(i in 1:N) {
y[i] ~ dnorm(mu[i], inv.sigma2)
mu[i] <- alpha - beta*pow(gamma, x[i])
res[i] <- (y[i] - mu[i])/sigma
p.res[i] <- phi(res[i])
}
alpha ~ dunif(0, 100)
beta ~ dunif(0, 100)
gamma ~ dunif(0, 1)
inv.sigma2 <- 1/pow(sigma, 2)
log(sigma) <- log.sigma
log.sigma ~ dunif(-10, 10)
}

Inits:
list(alpha = 3, beta = 2, gamma = 0.9, log.sigma = -5)

Data:
list(x = c(1.0, 1.5, 1.5, 1.5, 2.5, 4.0, 5.0, 5.0, 7.0,
8.0, 8.5, 9.0, 9.5, 9.5, 10.0, 12.0, 12.0, 13.0,
13.0, 14.5, 15.5, 15.5, 16.5, 17.0, 22.5, 29.0, 31.5),
y = c(1.80, 1.85, 1.87, 1.77, 2.02, 2.27, 2.15, 2.26, 2.47,
2.19, 2.26, 2.40, 2.39, 2.41, 2.50, 2.32, 2.32, 2.43,
2.47, 2.56, 2.65, 2.47, 2.64, 2.56, 2.70, 2.72, 2.57),
N = 27)

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   alpha   2.652   0.07177   0.001676   2.53   2.646   2.807   1001   50000
   beta   0.9735   0.07623   8.835E-4   0.8263   0.9719   1.13   1001   50000
   gamma   0.8623   0.03217   6.676E-4   0.7885   0.8657   0.9147   1001   50000

[example-8_3_3-dugongs0][example-8_3_3-dugongs1]