Respuesta :
To make the equation lets us find the rate of change of the weight
The form of the equation is y = m x + b
where:
m is the rate of change (slope)
b is the y-intercept (value y when x = 0)
To find m use two-point from the table
(1, 223.4) , (2, 221.8)
[tex]m=\frac{221.8-223.4}{2-1}=-\frac{8}{5}=-1.6[/tex]Substitute it in the form of the equation
[tex]y=-1.6x+b[/tex]To find b use any point in the table
(1, 223.4)
x = 1 , y = 223.4
[tex]\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}[/tex]Add 1.6 for both sides to find b
[tex]\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}[/tex]Substitute value b in the equation
[tex]y=-1.6x+225[/tex]The equation of the sequence is y = -1.6 x + 225
to find his weight after 16 weeks substitute x by 16
[tex]\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}[/tex]His weight after 16 weeks is 199.4 Ibs
