glm - Prediction of Exponential Decay or Logistic Growth in R -

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i'm trying predict in r, , i'm not sure syntax should use. know that, polynomial, can do:

predict(glm(y ~ x +i(x^2) + i(x^3) +... i(x^n),data=mydata))

which have been successful with, wondering how predict equations of form

y = c(1-e^(-kx))

or

y = a/(1 + b*e^(-kx)), k>0

i'm not sure example data can give illustrate well...

an example:

    set.seed(1234)     # parameters simulated data     c<-1     k<-2     # set x values , compute y them     x<-seq(-100,120,1)/100     y<-c*(1-exp(-k*x))+rnorm(length(x),sd=0.1)     # plot points     plot(x,y); grid()     # fit     fit<-nls(y ~ c*(1-exp(-k*x)), data=data.frame(y,x), start=list(c=5,k=5))     # plot fit     lines(x, predict(fit, list=(x=x)), col="red")

result:

    > fit     nonlinear regression model       model: y ~ c * (1 - exp(-k * x))        data: data.frame(y, x)         c     k      1.022 1.987       residual sum-of-squares: 2.147      number of iterations convergence: 8      achieved convergence tolerance: 1.338e-07

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