Question

Hello can you please help me with this problem I don't know understand how to do it?

Answer 1

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:

`m=(62.5-56.1)/(2-1)=(6.4)/(1)=6.4`

Substitute with (m), so the equation will be:

`G=6.4t+b`

Substitute with (t = 1, G = 56.1) to find (b)

`\begin{gathered} 56.1=6.4\cdot1+b \\ b=56.1-3.4=49.7 \end{gathered}`

So, the equation will be:

`G=6.4t+49.7`

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,

`G=6.4\cdot17+49.7=158.5`

So, the number of golden retrievers = 158.5 thousand