Question

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?

Answer 1

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).

Answer 2

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.