Question

Statistical models predict that the price (in dollars) of a 500 GB hard drive will change according to the function p(t) = 600 − 2t2, where t is the month. Which expression gives the number of months t (passed since January 1) in terms of the price p?

Answer 1

Answer:

$t(p)=\sqrt{\frac{1}{2}(600-p)}$

Step-by-step explanation:

Here, the expression that gives p in term of t is,

$p(t)=600-2t^2$ -----(1)

Where, p represents the price and t represents the number of months t (passed since January 1).

From equation (1),

$p=600-2t^2$

$2t^2=600-p$

$t^2=\frac{1}{2}(600-p)$

$t=\pm \sqrt{\frac{1}{2}(600-p)}$

But, number of months can not be negative,

$\implies t=\sqrt{\frac{1}{2}(600-p)}$

Since, in this expression t is in the term of p,

Hence, the required expression that gives the number of months t in terms of the price p is,

$t(p)=\sqrt{\frac{1}{2}(600-p)}$

Answer 2

Let p be a fixed value of price. The expression for t given a value of p is as follows:

$p=600-2t^2\\2t^2 = 600-p\\t^2 = \frac{600-p}{2}\\|t| = \sqrt{\frac{600-p}{2}}\\t=\sqrt{\frac{600-p}{2}},\,\,\,\,\,\,t\geq 0,\,\,p\leq 600$