Given:
In 2001, the number of registrations = 56.1 thousand
In 2002, the number of registrations = 62.5 thousand
We will write the linear equation to represents the given situation
Let G the number of registrations
And t is the number of years where t = 0 is the year 2000
So, in year 2001, t = 1, G = 56.1
And in year 2002, t = 2, G = 62.5
The general form of the equation will be: G = m * t + b
Where: (m) is the slope
and (b) is the y-intercept which will be the number of registrations at t = 0
We will find the slope as follows:
[tex]m=\frac{62.5-56.1}{2-1}=\frac{6.4}{1}=6.4[/tex]Substitute with (m), so the equation will be:
[tex]G=6.4t+b[/tex]Substitute with (t = 1, G = 56.1) to find (b)
[tex]\begin{gathered} 56.1=6.4\cdot1+b \\ b=56.1-3.4=49.7 \end{gathered}[/tex]So, the equation will be:
[tex]G=6.4t+49.7[/tex]B) Graph the equation:
The graph of the equation will be as shown in the following picture:
C) we will find the number of registrations in 2017
so, t = 2017 - 2000 = 17
So, substitute with (t=17) into the equation to find G
so,
[tex]G=6.4\cdot17+49.7=158.5[/tex]So, the number of golden retrievers = 158.5 thousand
