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

Question

I know that they grow at the same rate because they are both raised to the same power, but i don't know how to show it.

Answer 1

well, what is the rate of growth from x=a to x=b ?

2000b^4 / 2000a^4 = (b/a)^4

same for 200x^4

Answer 2

another way is we can say f(x) grows faster than g(x) as x>>inf if lim(x>inf) f(x)/g(x) = inf
if the limit approaches some constant k, they are growing at the same rate.

Lim(x>inf)=2000x^4/200x^4= 10
so they have the same growth rate.