Show that f(x) = 2000x^4 and g(x) = 200x^4 grow at the same rate.

I’ll be a junior in high school next year and i’m aiming for top colleges like northwestern university, princeton, stanford, etc. i’m worried my schedule for next year isn’t challenging enough in the eyes of top colleges. my courses next year are: ap english lit, ap psychology, english 3 hn, pre-calculus hn, us history (only offered at an average level or ap which is a 2 semester course), physics (same reasoning as us history), students in action (a class centered around volunteer work), and creative writing (i want to major in creative writing or literature). is this a “challenging” junior year? i’m on the varsity swim team and i have a part-time job so i don’t want to overwork myself. i also have limited space in my schedule and can’t take both ap us history and ap physics (both are 2 semesters). i can always take ap biology (2 semester class) and get rid of both physics and us history altogether (i’d rather take ap bio than ap physics and i can easily take physics senior year) but i’d have to take us history online because it’s a required junior class. it all comes back around to i need us history no matter what.