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You have repeated measurements data, and should fit a growth model. There will probably be some kind of serial correlation you should take into account. Your two factors seems to be time and concentration, you could try a polynomial in time. There are many similar posts here you can use as examples, for instance Do statisticians assume one can't over-...


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Does adding a level 1 time-varying predictor make the model non-linear?' No, the model is a linear model - this means that it is linear in the parameters. Of course, it is perfectly normal to model non-linear associations with a linear model. There is no reason to expect that the predictions will lie on a straight line after you introduce another variable. ...


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I'll assume that $g>0$ (because otherwise this does not make sense). The mean is usually defined as the number $\bar{y}$ such that $$ (b-a)\bar{y} = \int_a^b kg^t\,dt $$ (i.e., the rectangle with height $\bar{y}$ has the same area as there is under your function, in both cases betwee $t=a$ and $t=b$), or $$ \bar{y} = \frac{1}{b-a}\int_a^b kg^t\,dt. $$ ...


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