Solve the Problem $\mathrm { V } ( \mathrm { t } ) = - 0.0306 \mathrm { t } ^ { 3 } + 0.373 \mathrm { t } ^ { 2 } - 2.16 \mathrm { t } + 15.1$

Essay

Solve the problem.
-A team of engineers is testing an experimental high-voltage fuel cell with a potential application as an emergency back-up power supply in cell phone transmission towers. Unfortunately, the voltage of the prototype cell drops with time according to the equation $\mathrm { V } ( \mathrm { t } ) = - 0.0306 \mathrm { t } ^ { 3 } + 0.373 \mathrm { t } ^ { 2 } - 2.16 \mathrm { t } + 15.1$ , where $\mathrm { V }$ is in volts and $t$ is the time of operation in hours. The cell provides useful power as long as the voltage remains above $< \mathrm { v } >$ volts. Use Newton's method to find the useful working time of the cell to the nearest tenth of an hour (that is, solve $\mathrm { V } ( \mathrm { t } ) = 7.4$ volts). Use $\mathrm { t } = 7$ hours as your initial guess and show all your work.