A series electrical circuit for a computer game which you are testing, features a capacitor (C) discharging via a 270 kΩ resistor (R). The capacitor is initially charged to a voltage of 15 V. The voltage across the capacitor (Vc) may be described by the following equation, where t represents time.
Vc = 15 e−𝑡𝑡
𝑅𝑅𝑅𝑅
The circuit produces an output based upon the time it takes for the voltage on the capacitor to discharge to a
value of 2 V. The value of the capacitance is based upon the year of your birth, which is input at the start of the
game. For example, if you were born in 1987, then C = 1 + 9 + 8 + 7 = 25 μF.
Determine how long it takes for the circuit to produce an output.