I guess they assigned you this task because none of them have a clue how to do it. I'll give you help in two steps.
Tell me, what is the step response of a series RC circuit when there is no voltage on the capacitor.
Tell me, in a series RC circuit with the voltage on the capacitor equal to the supply voltage what is the step resonse when the switch to the supply is opened.
Express the results V(t) = ... where V(t) is a function of time, t and Vo, R, and C are parameters.
Some other spoilsport will probably just give you the answer in which case you will have learned nothing.