Question

mochi the panda cub has been measured and weighed each week since she was born.weeks weight 0. 11. 52. 93. 13Mochi brother is kapppa.his weight has been charted on the graph.which panda was heavier when they are born?which panda is growing faster?which panda will weigh more at 5 weeks?

Answer 1

We need to find the linear equations to model the growth of both Mochi and Kappa.

The general form of the equation in slope-intercept form is given by

`y=mx+b`

Here m is the slope of the equation and it represents the growth rate of the panda.

Here b is the y-intercept of the equation and it represents the weight of the panda when it was born.

Equation for Mochi:

The slope can be found by choosing any two points from the given table.

`m=(y_2−y_1)/( x_2−x_1)=(5-1)/(1-0)=(4)/(1)=4`

So, the equation becomes

`y=4x+b`

The y-intercept (b) can be found by choosing any point form the given table and substituting it into the above equation

`\begin{gathered} y=4x+b \\ 5=4(1)+b \\ 5=4+b \\ b=5-4 \\ b=1 \end{gathered}`

So the equation for Mochi is

`y=4x+1\quad eq.1_{}`

Equation for Kappa:

For kappa, we don't have the table but we are given the graph.

We can select any two points from the graph to find the slope of the equation.

Let us select the following points from the graph,

(0, 2) and (2, 8)

`m=(y_2−y_1)/(x_2−x_1)=(8-2)/(2-0)=(6)/(2)=3`

So, the equation becomes

`y=3x+b`

The y-intercept (b) can be directly found from the graph, it is the value of y-coordinate when x = 0

From the graph, we see that at x = 0 the value of y is 2

So, the equation for Kappa is

`y=3x+2_{}\quad eq.2`

Now let us answer the questions.

1. which panda was heavier when they are born?

We know that the y-intercept (b) of the equation represents the weight of the panda when it was born.

Since the y-intercept of the Kappa (that is 2 pounds) is greater than Mochi (that is 1 pound), therefore, Kappa was heavier.

2. which panda is growing faster?

We know that the slope of the equation represents the growth rate of the panda.

Since the slope of the Mochi (that is 4) is greater than Kappa (that is 3), therefore, Mochi is growing faster.

3. which panda will weigh more at 5 weeks?

Mochi's weight at 5 weeks:

`y=4x+1=4(5)+1=20+1=21\: lb`

Kappa's weight at 5 weeks:

`y=3x+2=3(5)+2=15+2=17\: lb`

Therefore, Mochi will weigh more at 5 weeks (that is 21 pounds)