Show that the population is always increasing. (Hint: Show b'(t) > 0 for all t > 0)
a) b'(t) < 0 for all t > 0
b) b'(t) = 0 for all t > 0
c) b'(t) > 0 for all t > 0
d) b'(t) is not defined for all t > 0