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The transient behaviour of a capacitor has been studied by measuring the voltage from across the device as a function of time. The following data has been obtained.

Time (s)/Voltage (v)

0 / 10

1 / 6.1

2 / 3.7

3 / 2.2

4 / 1.4

5 / 0.8

6 / 0.5

7 / 0.3

8 / 0.2

9 / 0.1

10 /0.07

12 /0.03

2. Homework Equations

The following relationship for the change in voltage, V, with time, t, has been proposed:

DV/DT = -k fcn(v)

Where k is a constant and fcn(v) could have one of the following forms:

1. fcn(v) = c (where c is a constant)

2. fcn(v) = V

3. fcn(v) = V2

(fcn is an abbreviation of the term "a function of")

I am to derive three corresponding expressions for V as a function of time.

3. The Attempt at a Solution

I am having trouble with where to start. I believe the aim is to find which equation, using the data, creates a linear relationship. Any help on how to derive the equations would be much appreciated.