Problem statement:

In a circuit with impressed voltage E(t) and inductance L, Kirchhoff's first law gives the relationship:

where R is the resistance in the circuit and i is the current. Suppose we measure the current for several values of t and obtain:

t | i

1.00 | 3.10

1.01 | 3.12

1.02 | 3.14

1.03 | 3.18

1.04 | 3.24

where t is measured in seconds, i is in amperes, the inductance L is a constant 0.98 henries, and the resistance is 0.142 ohms. Approximate the voltage E(t) when t = 1.00, 1.01, 1.02, 1.03, and 1.04.

Question:

I have been looking at this problem for a couple of days. I am unsure of where to begin with this. Can anyone give me a hint or advice to get this problem started?