A mobile phone manufacturer has to upgrade the circuitry in one of its products. Currently, the voltage in the signal-capture circuit rises according to the exponential function model [math]V(t) = 8(1 – e^{–at})[/math], in which [math]a[/math] is a positive constant and the coefficient of [math]t[/math], the time in seconds, and [math]V[/math] is the circuit voltage in volts. The graph shows how the voltage increases when a cell-phone tower signal is detected for [math]a = 1[/math].
How will the function model have to be modified if the upgraded phone circuit has a voltage “rise time” that results in a circuit voltage of at least 7.9 volts in less than 1 second when a cell-phone tower signal is detected?
