You are given the function [tex]p=900-4t^2.[/tex]
Express t:
[tex]4t^2=900-p,\\\\t^2=\dfrac{900-p}{4},\\\\t=\sqrt{\dfrac{900-p}{4}}.[/tex]
This expression gives the month t in terms of the price p.
Answer:
The expression [tex]\sqrt{\frac{p-900}{4}}[/tex] 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 [tex]p=900-4t^2[/tex]
We have to find the expression which gives the number of month t in terms of the price.
Consider the given function [tex]p=900-4t^2[/tex]
Since, we have to find the expression for t , we have,
[tex]p=900-4t^2[/tex]
Subtract 900 both side, we have,
[tex]p-900=-4t^2[/tex]
Divide both side by 4, we have,
[tex]\frac{p-900}{4}=t^2[/tex]
Taking square root both side, we have,
[tex]\sqrt{\frac{p-900}{4}}=t[/tex]
Thus, The expression [tex]\sqrt{\frac{p-900}{4}}[/tex] gives the number of month t in terms of the price.
