Chapter 1, Problem 63SGR

To determine

To calculate: The number of plants growing for 50, 100, 150 and 200 seeds if on average 7 plants grow for every 10 seeds also domain and range of the relation represented by situation. Also sketch the graph of the relation.

Answer to Problem 63SGR

The domain of the relation is $\left\{50,100,150,200\right\}$ and range is $\left\{35,70,105,140\right\}$ . Tabular representation of relation is,

  $\begin{array}{cc}x& y\\ 50& 35\\ 100& 70\\ 150& 105\\ 200& 140\end{array}$

Graph of the relation is provided below,

  

Explanation of Solution

Given information:

In a garden on average 7 plants grow for every 10 seeds.

Formula used:

A relation is a set of ordered pairs of the form $\left(x,y\right)$ , where x is the element of domain and y is the element of range.

Calculation:

Consider the provided information that in a garden on average 7 plants grow for every 10 seeds.

Denote the number of seeds as x and number of plants as y .

According to the question, 7 plants grow for every 10 seeds.

Therefore, one plant will grow for $\frac{7}{10}$ seeds.

So, mathematically it expressed as, $y=\frac{7}{10}x$ .

Therefore, the number of plants growing for 50, 100, 150 and 200 seeds are,

Substitute x as 50, 100, 150 and 200 in the relation $y=\frac{7}{10}x$ to compute number of plants.

Tabular representation of the same is provided below,

  $\begin{array}{cc}x& y\\ 50& 35\\ 100& 70\\ 150& 105\\ 200& 140\end{array}$

To express the relation as a graph, plot each ordered pair $\left(50,35\right),\left(100,70\right),\left(150,105\right),\left(200,140\right)$ of the relation on a coordinate plane.

Graphical representation of relation is provided below,

  

Now, domain of the relation is the set of all x -coordinates of ordered pair and range is the set of all y -coordinates of ordered pair.

Therefore, domain of the relation is $\left\{50,100,150,200\right\}$ and range is $\left\{35,70,105,140\right\}$ .