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:

Cancer Cells

Abnormal cells that divide uncontrollably, have the ability to infiltrate and destroy normal body tissue, and can spread to other parts of the body.

Mutations

Changes in the DNA sequence of an organism's genome, which can lead to variations in physical traits or an increase in susceptibility to certain diseases.

Socioeconomic Status

An individual's or family's economic and social position in relation to others, based on income, education, and occupation.

Cancer Rates

The incidence or number of new cases of cancer per population in a specified period.