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

question 182

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.

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Definitions:

Independent Variable

In a scientific experiment, the variable that the researcher modifies or controls to investigate its influence on the dependent variable.

Correlations

A measure indicating the level at which multiple variables exhibit joint variability.

Systematic Problem-Solving

An approach to addressing issues that involves defining the problem, analyzing the problem, generating potential solutions, evaluating and selecting the best solution, and implementing the solution.

Robert Sternberg

An American psychologist known for his theory on intelligence and creativity, including the triangular theory of love.