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 where 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 5.1 volts. Use Newton's method to find the useful working time of the cell to the nearest tenth of an hour (that is, solve V(t) = 5.1 volts). Use t = 7 hours as your initial guess and show all your work.

Question

What will be an ideal response?

Answer 1

Find the root of f(x) = -0.0306t³ + 0.373t² - 2.16t + 15.1 - 5.1.

f'(x) = -0.0918t² + 0.746t - 2.16

x₁ = 7
x₂ = 7 -  = 7 -  = 8.85
x₃ = 8.85 -  = 8.85 -  = 8.45

The useful working time is t = 8.45 hours.