Here are some scholarly links on the brain health effects of exercise.
http://resulb.ulb.ac.be/facs/ism/docs/behaviorBDNF.pdf
"Plasticity" is a fancy word for learning, and improving the capacity to learn
The Acute Effects of a Single Bout of Moder... [J Clin Diagn Res. 2013] - PubMed - NCBI
"Improvement in executive functions has also been reported during
cycling at 70% of Heart Rate Reserve (HRR) across young and older age groups."
"A single bout of moderate intensity aerobic exercise for as less [sic]as 30 minutes can improve some aspects of cognition, most prominently for memory, reasoning and planning and can shorten the time taken to complete the tests. " (Even articles in the US national science library can have grammatical errors)
Voluntary exercise increases axonal... [Proc Natl Acad Sci U S A. 2004] - PubMed - NCBI Exercise stimulates nervous system recovery from injury (outside the brain, in this case).