R curvefit [REAT]: What are the equations of the nonlinear functions?

Question

I am trying to fit curves to my data with the curvefit() function of the REAT package. The results look good and give me a table like this:

                       a           b Std. Error a Std. Error b  t value a t value b
Linear      -1494.108840 166.1867222  523.5387976  30.50266009 -2.8538646  5.448270
Power           0.425234   2.7725836    0.4456762   0.36780235 -0.8332776  7.538243
Exponential    32.008316   0.2022666    0.4492831   0.02617634  7.7145024  7.727078
Logistic        7.076363  -0.4071710    1.6305232   0.09499830  4.3399340 -4.286087

              Pr(>|t|) a   Pr(>|t|) b R squared Adj. R squared  F value       Pr(>F)
Linear      1.275234e-02 8.582766e-05 0.6795139      0.6566221 29.68364 8.582766e-05
Power       4.186780e-01 2.716813e-06 0.8023300      0.7882107 56.82511 2.716813e-06
Exponential 2.085140e-06 2.046447e-06 0.8100606      0.7964935 59.70773 2.046447e-06
Logistic    6.790587e-04 7.535634e-04 0.5675080      0.5366157 18.37054 7.535634e-04

What I would like to do is to extract the functional equations of the curves. For linear fit, this is probably y = ax + b . But which functions are used for the other three?

In the function code I found lm (log10(y) ~ log10(x)) for power, lm (log(y) ~ x) for exponential and lm ( (log((y.max-y)/y)) ~ x) for logistic.

Probably due to my faded maths skills, I don't know how to derive a function including the paramters a and b, just like the one for linear regression. Therefore, any help is appreciated.

Answer 1

Tried around a lot and found out this:

Linear: y = b*x + a

Power: y = a*x^b

Exponential: y = a*exp(b*x)

I am still missing the logistic function though, if someone knows it.