1. Show that f(x) = x^2and g(x) = 1000x^2grow at the same rate.
2. Water is poured into a bucket according to the rateF(t)= t+7/2+t, and at the same time empties out through a hole in the bottom at the rate E(t)=ln(t+4)/t+2, with both F(t) and E(t) measured in pints per minute. How much water, to the nearest pint, is in the bucket at time t = 5 minutes. You must show your setup but can use your calculator for all evaluations.