Chapter 4.1, Problem 31PPS

a.

To determine

To find: Number of thousands of golden retrievers G as a function t in slope intercept form.

Answer to Problem 31PPS

  $G=6.4t+49.7$

Explanation of Solution

Given information:

At $t=0$ it means year is 2000

  $G=56.1$ thousand at $t=1$

  $G=62.5$ thousand at $t=2$

slope intercept form of a line is

  $G=mt+b$

Substituting t=1 and G=56.1

We get

  $56.1=m+b$ --------(1)

Substituting t=2 and G=62.5

We get

  $62.5=2m+b$ ------(2)

Subtracting equation (2) − equation (1)

We get

  $\begin{array}{l}\Rightarrow 62.5-56.1=2m+b-(m+b)\\ \Rightarrow 6.4=2m+b-m-b\\ \Rightarrow m=6.4\end{array}$

Put value of m in equation (1)

We get

  $\begin{array}{l}\Rightarrow 56.1=m+b\\ \Rightarrow 56.1=6.4+b\\ \Rightarrow b=56.1-6.4\\ \Rightarrow b=49.7\end{array}$

Therefore

Slope intercept form is $G=6.4t+49.7$

b.

To determine

To find: Number of golden retrievers that will be registered in $2027$ .

Answer to Problem 31PPS

Number of golden retrievers registered in 2027 is $G=222.5$

Explanation of Solution

Given information:

At $t=0$ it means year is 2000

  $G=56.1$ thousand at $t=1$

  $G=62.5$ thousand at $t=2$

For year 2027 time will be $t=27$

on substitute $t=27$

we get

  $\begin{array}{l}G=6.4t+49.7\\ \Rightarrow G=6.4(27)+49.7\\ \Rightarrow G=172.8+49.7\\ \Rightarrow G=222.5\end{array}$

Therefore

Number of golden retrievers registered in 2027 is $G=222.5$