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#' Indeterminate order rate equation kinetics
#'
#' Function describing exponential decline from a defined starting value, with
#' a concentration dependent rate constant.
#'
#' @param t Time.
#' @param parent.0 Starting value for the response variable at time zero.
#' @param k__iore Rate constant. Note that this depends on the concentration
#' units used.
#' @param N Exponent describing the nonlinearity of the rate equation
#' @return The value of the response variable at time \code{t}.
#' @note The solution of the IORE kinetic model reduces to the
#' \code{\link{SFO.solution}} if N = 1. The parameters of the IORE model can
#' be transformed to equivalent parameters of the FOMC mode - see the NAFTA
#' guidance for details.
#' @references NAFTA Technical Working Group on Pesticides (not dated) Guidance
#' for Evaluating and Calculating Degradation Kinetics in Environmental Media
#' @keywords manip
#' @examples
#'
#' plot(function(x) IORE.solution(x, 100, 0.2, 1.3), 0, 2, ylim = c(0, 100))
#' \dontrun{
#' fit.fomc <- mkinfit("FOMC", FOCUS_2006_C, quiet = TRUE)
#' fit.iore <- mkinfit("IORE", FOCUS_2006_C, quiet = TRUE)
#' fit.iore.deS <- mkinfit("IORE", FOCUS_2006_C, solution_type = "deSolve", quiet = TRUE)
#'
#' print(data.frame(fit.fomc$par, fit.iore$par, fit.iore.deS$par,
#' row.names = paste("model par", 1:4)))
#' print(rbind(fomc = endpoints(fit.fomc)$distimes, iore = endpoints(fit.iore)$distimes,
#' iore.deS = endpoints(fit.iore)$distimes))
#' }
#'
#' @export
IORE.solution <- function(t, parent.0, k__iore, N)
{
parent = (parent.0^(1 - N) - (1 - N) * k__iore * t)^(1/(1 - N))
}
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