Answer :
We are given the regression equation
[tex]$$
y = 8.6 \sin (0.24x - 1.88) + 62.8.
$$[/tex]
This equation represents the Fahrenheit temperature, where the sine part is multiplied by an amplitude of [tex]$8.6$[/tex] and then shifted vertically by [tex]$62.8$[/tex]. The sine function has a maximum value of [tex]$1$[/tex]. Therefore, the maximum value of the entire function occurs when
[tex]$$
\sin(0.24x - 1.88) = 1.
$$[/tex]
At this point, the temperature is
[tex]$$
y_{\text{max}} = 8.6 \times 1 + 62.8 = 8.6 + 62.8 = 71.4.
$$[/tex]
Thus, the maximum temperature in the room during the first 24 hours is
[tex]$$
71.4^{\circ}F.
$$[/tex]
[tex]$$
y = 8.6 \sin (0.24x - 1.88) + 62.8.
$$[/tex]
This equation represents the Fahrenheit temperature, where the sine part is multiplied by an amplitude of [tex]$8.6$[/tex] and then shifted vertically by [tex]$62.8$[/tex]. The sine function has a maximum value of [tex]$1$[/tex]. Therefore, the maximum value of the entire function occurs when
[tex]$$
\sin(0.24x - 1.88) = 1.
$$[/tex]
At this point, the temperature is
[tex]$$
y_{\text{max}} = 8.6 \times 1 + 62.8 = 8.6 + 62.8 = 71.4.
$$[/tex]
Thus, the maximum temperature in the room during the first 24 hours is
[tex]$$
71.4^{\circ}F.
$$[/tex]
