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.

Every tissue in the human body has its own T1 and T2 value. This term is used to indicate an image where most of the contrast between tissues is due to differences in the T1 value.
This term may be misleading in that the potentially important effects of tissue density differences and the range of tissue T1 values are ignored.
If the machine parameters are chosen, so that TR less than T1 (typically under 500 ms) and TE less than T2 (typically under 30 ms), a power series expansion of the exponential functions and then neglecting second and higher order terms yields
Mxy = Mxy0 TR/T1
thus the expression becomes independent of T2 and yields the condition for T1 weighting. Therefore a T1 contrast is approached by imaging with a short TR, compared to the longest tissue T1 of interest and short TE, compared to tissue T2 (to reduce T2 contributions to image contrast). Due to the wide range of T1 and T2 and tissue density values that can be found in the body, an image that is T1 weighted for some tissues may not be so for others.
Lesions with short T1 are (bright in T1 weighted sequences):
fat (lipoma, dermoid)
sub-acute haemorrhage (metHb)
paramagnetic agent (Gd, pituitary)
protein-containing fluid (colloid cyst)
metastatic melanoma (melanotic).