The purpose of the study is to see if daily use of nicotine patches will slow or reverse memory loss in participants with Mild cognitive impairment, an early stage of mental decline associated with Alzheimer's disease. Nicotine may mimic natural chemicals in the brain that play a crucial role in memory function, and previous studies have shown that nicotine may improve attention, learning, and memory. In this study, participants will receive either nicotine (up to 21mg/day, the standard dosage of a nicotine patch) or placebo for 2 years to see if these improvements in brain function can be observed over a longer period.