A capacitor with capacitance C 0 , after having been connected to a battery with emf 0 for a long time, is discharged through

A capacitor with capacitance C₀, after having been connected to a battery with emf ξ₀ for a long time, is discharged through a 200 000Ω resistor at time t = 0. The potential difference across the capacitor is measured as a function of time for a brief time interval; the results are recorded below.

(a) Write an equation that describes the potential difference across the capacitor as a function of time. Enter the data into your calculator and have the calculator perform a linear regression fit of in V_C versus t. From the parameters of the fit, determine

(b) The emf ξ₀ of the battery and

(c) The time constant τ for the circuit. 

(d) Finally, determine the value of capacitance C₀.