Each curve in the figure below represents the balance in a bank account into which a single deposit was made at time zero.

graph of four increasing exponential functions, labeled I-IV. II and IV start at the same y-intercept, but IV grows faster. III starts at a higher y-intercept, and grows to a value between II and IV. I starts at a still higher y-intercept, and finishes below II.

Assuming continuously compounded interest, find (enter each answer as value or a list, e.g, I or II,III): :
(a) The curves representing the same initial deposit :
(b) The curve(s) representing the smallest initial deposit :
(c) The curves representing the same interest rate :
(d) The curve(s) representing the smallest interest rate :

You can earn partial credit on this problem.