Respuesta :
The number of months t in terms of the price p exists,
[tex]$t(p)=\sqrt{\frac{1}{2}(600-p)}[/tex].
Which expression gives the number of months t (passed since January 1) in terms of the price p?
Here, the expression that gives p in terms of t is,
[tex]$p(t)=600-2 t^{2} \ldots(1) $[/tex]
Where p denotes the price and t denotes the number of months t
(passed since January 1).
From equation (1),
[tex]${data-answer}amp;p=600-2 t^{2} \\[/tex]
[tex]${data-answer}amp;2 t^{2}=600-p \\[/tex]
[tex]${data-answer}amp;t^{2}=\frac{1}{2}(600-p) \\[/tex]
[tex]${data-answer}amp;t=\pm \sqrt{\frac{1}{2}(600-p)}[/tex]
But, the number of months cannot be negative,
[tex]$\Longrightarrow t=\sqrt{\frac{1}{2}(600-p)}$[/tex]
Since, in this expression, t exists in the term of p
Hence, the necessary expression that gives the number of months t in terms of the price p exists,
[tex]$t(p)=\sqrt{\frac{1}{2}(600-p)}[/tex]
Therefore, the correct answer is option c)\sqrt(300-p).
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