Posted by nico on .
A 12,000 liter tank filled to capacity at t=0 drains at rate r(t), measured in liters per hour, where r is defined as piecewise function:
r(t)={ (600t)/(t+3), [0,5]
{1000e^(0.2t), (5,infinity)
Is r continuous at t=5? Show work that lead to you answer.

calculus 
Steve,
at t=5,
600t/(t+3) = 3000/8 = 375
1000e^(.2t) = 1000/e = 367.8
Actually, the computation isn't really necessary, since r(t) is rational at t=5, and e^x is irrational for any rational x. 
calculus 
nico,
what does your answer mean exactly?

calculus 
Steve,
it means that the two piecewise functions don't have the same value at t=5, so r(t) cannot be continuous.