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# Sinuosodal Equation

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The size of a certain population of wild horses varies because of certain ecological pressures. In 1999, the number of horses was 100. In 2002, the population was down to 60, but in 2005, the population was back up to 100.

Assume that 100 was the maximum number of horses and 60 was the minimum. Write an equation that models the size of the population of horses, in terms of what year it is, starting with 1999.

I know f(x) = 20sin(k(x)) + 80 and it is 20sin(πx / 3 + π / 2) + 80 but I need the equation in degrees instead of radian

Dec 5, 2018

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The size of a certain population of wild horses varies because of certain ecological pressures.
In 1999, the number of horses was 100.
In 2002, the population was down to 60,
but in 2005, the population was back up to 100.

Assume that 100 was the maximum number of horses and 60 was the minimum.
Write an equation that models the size of the population of horses,
in terms of what year it is,
starting with 1999.

$$\text{Let x is the year}$$

$$\begin{array}{|rcll|} \hline f(x) &=& 20\sin\left(\frac{\pi}{3}(x-1999) + \frac{\pi}{2} \right ) + 80 \quad & | \quad \pi \mathrel{\hat{=}} 180^{\circ} \\\\ &=& 20\sin\left(\frac{180^{\circ}}{3}(x-1999) + \frac{180^{\circ}}{2} \right ) + 80 \\ \mathbf{f(x)} & \mathbf{=} & \mathbf{ 20\sin( 60^{\circ}(x-1999) + 90^{\circ} ) + 80 } \\ \hline \end{array}$$

Dec 5, 2018