This corpus study examines entropy via the model of perplexity in regards to the spontaneous speech of adults as they age, and compares this with the overall entropy of speech produced by those with Alzheimer's disease. Switchboard and Buckeye corpora were used for typical adult speech, and Alzheimer's speech came from the Carolina Conversations Collection. Two language models, one containing speech from adults under 40 and one containing speech from those over 40, were created in the SRI Language Modeling Toolkit and used to calculate perplexity from individuals randomly taken from different decade spans in the Switchboard corpus and from 33 individuals with Alzheimer's from the CCC. Python NLTK was used to calculate various speech characteristics, such as mean length of utterance, type/token ratio, low specificity words, fillers, repetitions, and part of speech proportions. There was a general upward trend in perplexity as age increased, and this effect remained consistent in both the younger language model and the older language model. In terms of speech characteristics, mean length of utterance and usage of nouns had statistically significant effects in both the younger and the older language model.