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].[br][br]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?

[list=1][br][*]Write an inequality using the function that reflects the necessary conditions for a faster rise time.[br][*]Solve the resulting inequality.[br][*]Check the result of the previous step by substituting it into the original exponential function.[br][/list][br][br]This applet is provided by Walch Education as supplemental material for their mathematics programs. Visit [url=http://www.walch.com]www.walch.com[/url] for more information.