Yes, that is correct. "To the nearest mile" isn't all that accurate but if that was what you were told to do ....
Hailey has begun a fitness program. The first week she ran 1 mile every day. Each week she increases the amount that she runs each day by 20%. In week 10, how many miles does she run each day? Give your answer to the nearest mile.
My solution:
A=P(1+r)^n
=1(1.2)^9
=5