Given the table:
t B
1 22.5
3 13.5
5.5 2.25
Where B represents the charge remaining in Peyton's battery.
And t represents the number of hours since Peyton left her house.
Let's determine the number of hours it would take until the phine's battery level get down to 24.75%.
First of all, let's create a linear equation that is represented on the table.
Apply the slope intercept form of a linear equation:
y = mx + b
Where m is the slope.
To find the slope apply the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Take two points on the table:
(x1, y1) ==> (1, 22.5)
(x2, y2) ==> (3, 13.5)
Thus, we have:
[tex]\begin{gathered} m=\frac{13.5-22.5}{3-1} \\ \\ m=\frac{-9}{2} \\ \\ m=-4.5 \end{gathered}[/tex]To solve for b, susbtitute -4.5 for m, and input one of the points for the values of x and y:
[tex]\begin{gathered} y=mx+b \\ \\ 22.5=-4.5(1)+b \\ \\ 22.5=-4.5+b \\ \\ \text{Add 4.5 to both sides:} \\ 22.5+4.5=-4.5+4.5+b \\ \\ 27=b \\ \\ b=27 \end{gathered}[/tex]Therefore, the equation that represents this situation is:
y = -4.5x + 27
To find the number of hours it would take until the phone's battery level got down to 24.75%, substitute 24.75 for y in the equation and solve for x.
y = -4.5x + 27
24.75 = -4.5x + 27
Subtract 27 from both sides:
24.75 - 27 = -4.5x + 27 - 27
-2.25 = -4.5x
Divide both sides by -4.5:
[tex]\begin{gathered} \frac{-2.25}{-4.5}=\frac{-4.5x}{-4.5} \\ \\ 0.5=x \end{gathered}[/tex]Therefore, it would take 0.5 hour for the phone's battery level to get down to 24.75%.
ANSWER:
0.5