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Fractional Exponents

Relate fractional exponents to nth roots

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Practice Fractional Exponents

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Beaufort Scale
Teacher Contributed

Real World Applications – Algebra I

Topic

How can we use exponents to measure a wind storm at sea?

Student Exploration

If we look at the weather forecast on the news, there are many different ways that is explained to you. They usually tell us the temperature, the wind speed in your local area, and the humidity. At sea, the Beaufort Scale is usually used to determine how rough winds are, besides given in miles per hour.

If you look at this video,

we can see that the Beaufort Scale is about an 8 or 9. But what does that mean?

The Beaufort Scale is a formula that is used to determine the intensity of wind for hurricanes and tornados. A formula is used to intensity on the Beaufort scale and wind speed at 10 meters above the sea surface: v=0.836B(32)\begin{align*}v = 0.836B^\left(\frac{3}{2}\right)\end{align*}. “V\begin{align*}V\end{align*}” represents the wind speed at 10 meters above the sea surface, and “B\begin{align*}B\end{align*}” represents the Beaufort scale number. If the news anchor were to mention a “Beaufort 9,” should we run for shelter? Let’s use this formula to find out.

V=0.836(9)(32)\begin{align*}V = 0.836(9)^\left(\frac{3}{2}\right)\end{align*}

After doing all of the calculations, we find that v=22.572\begin{align*}v = 22.572\end{align*} meters per second. The type of damage that this type of wind might do is blow trees and signs over. Would you run for cover?

What if winds were 30 meters per second? Should we substitute 30 in for B\begin{align*}B\end{align*} or v\begin{align*}v\end{align*}?

Since we’re given the wind speed, we should substitute this into the equation for “v\begin{align*}v\end{align*}.”

30=0.836B(32)\begin{align*}30 = 0.836B^\left(\frac{3}{2}\right)\end{align*}

We first divide both sides by 0.836, and then square both sides and then take the cube root of both sides to solve for B\begin{align*}B\end{align*}.

300.83635.885(35.885)1287.7331287.733(13)10.879=B(32)=B(32)=B3=B3=B=B\begin{align*}\frac{30}{0.836} &= B^{\left(\frac{3}{2}\right)}\\ 35.885 &= B^{\left(\frac{3}{2}\right)}\\ \sqrt{(35.885)} &= B^3\\ 1287.733 &= B^3\\ 1287.733^{\left(\frac{1}{3}\right)} &= B\\ 10.879 &= B\end{align*}

10 is pretty high on the Beaufort Scale, especially since the numbers range from 0 to 12! At Beaufort 10, you’d expect a really violent storm with uprooted trees and shingles flying off roofs!

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