Statistics Solutions

[All Steps] Temperature During a summer thunderstorm, the temperature drops and then rises again. The rate of change of the temperature during the hour and

Question: Temperature During a summer thunderstorm, the temperature drops and then rises again. The rate of change of the temperature during the hour and a half after the storm began is given by

\(T(h)=9.5 h^{3}-15.5 h^{2}+17.4 h-10.12^{\circ} \mathrm{F}\) per hour

where \(h\) is the number of hours since the storm began.

  1. Graph the function \(T\) from \(h=0\) to \(h=1.5\). Find the point \(A\) at which the graph crosses the horizontal axis.
  2. Consider the portion of the graph of \(T\) lying below the horizontal axis. What does the area of the region between this portion of the graph of \(T\) and the horizontal axis represent?
  3. What does the area of the region lying above the axis represent?
  4. Consider the graph between 0 and $1.5$ hours. Use three right rectangles to approximate the area of the region lying below the axis from 0 to $1.5$ hours.
  5. Repeat part \(d\) for the region lying above the axis.
  6. Use a limit of sums to estimate \(\int_{0}^{A} T(h) d h\).
    Price: $2.99
    Solution: The downloadable solution consists of 3 pages
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