  In this paper, a cosmological solution to Mimetic Dark Matter (MDM) for an
exponential potential is provided. Then, a solution for the $0-i$ perturbed
Einstein's differential equation of MDM is obtained based on an exponential
potential that satisfies inflation for some initial conditions. Another general
potential is suggested that incorporates inflation too. Then, quantum
perturbations are included. The constants in the model can be tuned to be in
agreement with the amplitude fluctuation of the cosmic microwave background
(CMB) radiation. Finally, the spectral index is calculated for the suggested
potentials. Moreover, MDM is shown to be a viable model to produce dark matter,
inflation, and CMB's fluctuation.
