model {
for(j in 1:27) {
y[j] ~ dnorm(mu[j], tau)
mu[j] <- alpha - beta*pow(gamma, x[j])
# prior on covariate
x[j] ~ dlnorm(mu.x, p.x)
}
alpha ~ dunif(0, 100)
beta ~ dunif(0, 100)
gamma ~ dunif(0, 1)
tau <- 1/pow(sigma, 2)
log(sigma) <- log.sigma
log.sigma ~ dunif(-10, 10)
# priors on mean and precision of covariate model
mu.x ~ dunif(-10, 10)
p.x <- 1/pow(sd.x, 2)
sd.x ~ dunif(0, 10)
}

Inits:
list(alpha = 3, beta = 2, gamma = 0.9, log.sigma = -5, mu.x = 2, sd.x = 0.01)

Data:
list(x = c(1.0,1.5,1.5, NA ,2.5,4.0,5.0,5.0,NA,8.0,8.5,9.0,
9.5,9.5,10.0,12.0,12.0,13.0,NA,14.5,15.5,15.5,
16.5,17.0,NA,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))

   node   mean   sd   MC error   2.5%   median   97.5%   start   sample
   alpha   2.649   0.06845   0.001528   2.527   2.645   2.797   4001   50000
   beta   0.9604   0.07883   9.338E-4   0.8136   0.9584   1.116   4001   50000
   gamma   0.8661   0.03251   7.006E-4   0.7926   0.8707   0.9152   4001   50000
   mu.x   2.096   0.2087   9.875E-4   1.689   2.094   2.512   4001   50000
   sd.x   1.048   0.1722   0.001139   0.7735   1.027   1.444   4001   50000
   sigma   0.0955   0.01605   1.407E-4   0.07019   0.09341   0.1325   4001   50000
   x[4]   1.395   0.7006   0.004034   0.3363   1.299   3.035   4001   50000
   x[9]   16.7   18.08   0.1805   6.831   12.77   54.61   4001   50000
   x[19]   17.52   22.87   0.2601   6.821   12.88   59.72   4001   50000
   x[25]   38.5   39.62   0.3918   12.3   28.05   127.9   4001   50000