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statistical models predict that price p( in dollars) of a new smartphone will change according to the function p=900-4t^2. where t is the number of months since january. which expression gives the.month t in terms of the price?

2 Answers

5 votes

Final answer:

To express the month t in terms of the price p for a smartphone using the function p = 900 - 4t^2, rearrange the equation to solve for t, which results in t = √((900 - p) / 4), considering only the positive square root since months cannot be negative.

Step-by-step explanation:

The student's question asks to express the month t in terms of the price p for a smartphone based on the given function p = 900 - 4t2. To solve for t, we will rearrange the equation by isolating t2 on one side. Here's how we do it:

Start with the equation p = 900 - 4t2.

Add 4t2 to both sides: p + 4t2 = 900.

Subtract p from both sides: 4t2 = 900 - p.

Divide both sides by 4: t2 = (900 - p) / 4.

Finally, take the square root of both sides: t = ±√((900 - p) / 4).

However, since t represents the number of months, we only take the positive square root because time cannot be negative:

t = √((900 - p) / 4).

User Andrii Zarubin
by
7.8k points
1 vote

Answer:

The expression
\sqrt{(p-900)/(4)} gives the number of month t in terms of the price.

Step-by-step explanation:

Given : Statistical models predict that price p( in dollars) of a new smartphone will change according to the function
p=900-4t^2

We have to find the expression which gives the number of month t in terms of the price.

Consider the given function
p=900-4t^2

Since, we have to find the expression for t , we have,


p=900-4t^2

Subtract 900 both side, we have,


p-900=-4t^2

Divide both side by 4, we have,


(p-900)/(4)=t^2

Taking square root both side, we have,


\sqrt{(p-900)/(4)}=t

Thus, The expression
\sqrt{(p-900)/(4)} gives the number of month t in terms of the price.

User Pablo Maurin
by
8.6k points
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