An exponential function is a function of the form
f(x) = a^x
where a is a fixed, positive constant, called the base of the exponential function.
Exponential functions are used to express dynamic processes, also in MRI.

Multiplication of the time-dependent signal data by an exponential function, exp(t/TC), where t is time and TC is a parameter called the time constant (in spectroscopy). The time constant can be chosen to either improve the signal to noise ratio (with a negative TC) or decrease the effective spectral line width (with a positive TC) in the resulting spectrum. The use of a negative TC to improve SNR is equivalent to line broadening by convolving the spectrum with a Lorentzian function of corresponding reciprocal width.

The contrast agents are either renal or hepatically excreted media, which stay in the intravascular/extracellular tissue compartment. The enhancement in the blood continues for as long as the contrast agent remains in the blood stream.
E.g. Dotarem®, Magnevist®, Omniscan®, ProHance®.

See Contrast Medium, Contrast Agents and Blood Pool Agents.