  The paper discusses a particular model of chameleon gravity where the scalar
field has an exponential as $V=M^{4}\exp(\frac{\alpha\phi}{M_{pl}})$ and an
exponential coupling to the matter density component of the Universe as
$\rho_{m}\exp(\frac{\beta\phi}{M_{pl}})$. We finds the relations between the
four (in principle free) parameters of the model and the first five
cosmographic parameters (which can be written in terms of the Hubble parameter
and its first four derivatives). If such cosmographic parameter are known then
the we present the algebraic relations which can be used to derive the free
parameters in terms of the cosmographic ones. We show that, determining the
third derivative of scale factor $Q$ is of great importance if the chameleon
parameter $\beta$ and coupling constant $\alpha$ are known. On the other hand,
if nothing can be proposed about $(\alpha,\beta)$, reconstructing the free
parameters of the model can be done by measuring the first five derivatives of
the scale factor and testing the validity of theory is only possible by its
first six derivatives, so that the parameters $(\alpha,\beta)$ will also be
determined automatically. We also find relation between cosmographic parameters
and parameters of the model when it dynamically approaches its critical points.
