Professor Knopfloch/Intelligence development/Exercise

At the begin of the university studies, Professor Knopfloch is double as clever as the students. Within one year of studies, the students are getting more clever by a percentage of ${}10\%$. Unfortunately, the professor looses a percentage of ${}10\%$ of his cleverness each year.

1. Show that after three years of studies, the professor is still more clever that his students.
2. Show that after four years of studies, the students are more clever than the professor.

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