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?
[list=1] [*]Write an inequality using the function that reflects the necessary conditions for a faster rise time. [*]Solve the resulting inequality. [*]Check the result of the previous step by substituting it into the original exponential function. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math III[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.