Question

0 Rick has been losing weight at a constant rate since he began his new fitness plan. The table below shows Rick's weight for the first four weeks, 2 3 I 220.2 218.6 221.8 223.4 Weight (lbs) a) Write an equation to represent this sequence. b) Find Rick's weight after 16 weeks. ter your answer(s) here

Answer 1

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)

`m=(221.8-223.4)/(2-1)=-(8)/(5)=-1.6`

Substitute it in the form of the equation

`y=-1.6x+b`

To find b use any point in the table

(1, 223.4)

x = 1 , y = 223.4

`\begin{gathered} 223.4=-1.6(1)+b \\ 223.4=-1.6+b \end{gathered}`

Add 1.6 for both sides to find b

`\begin{gathered} 223.4+1.6=-1.6+1.6+b \\ 225=b \end{gathered}`

Substitute value b in the equation

`y=-1.6x+225`

The equation of the sequence is y = -1.6 x + 225

to find his weight after 16 weeks substitute x by 16

`\begin{gathered} y=-1.6(16)+225 \\ y=-25.6+225 \\ y=199.4 \end{gathered}`

His weight after 16 weeks is 199.4 Ibs