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 , in which is a positive constant and the coefficient of , the time in seconds, and is the circuit voltage in volts. The graph shows how the voltage increases when a cell-phone tower signal is detected for .
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?

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.

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