Chapter 1, Problem 67CR

To determine

To find: Total number of plants, growing for 50, 100, 150 and 200 seeds.

Answer to Problem 67CR

Total plants growing for 50, 100, 150, and 200 seeds are 35, 70, 105 and 140 respectively.

The domain of relation is $\{50,100,150,200\}$ and range is $\{35,70,105,140\}$

. The graph is shown below:

Explanation of Solution

Given information:

On average, 7 plants grow for every 10 seeds of a certain type planted.

Concept used:

First calculate unit rate i.e. total plants growing for 1 seed and then multiply this unit rate for given number of seeds.

Domain is the set of all seeds available and range is the set of all plants growing, respectively.

Calculation:

As plants growing for 10 seeds $=7$

So, plants growing for 1 seed $=\frac{7}{10}$

So plants growing for 50 seeds $=\frac{7\times 50}{10}=35$

Plants growing for 100 seeds $=\frac{7\times 100}{10}=70$

Plants growing for 150 seeds $=\frac{7\times 150}{10}=105$

Plants growing for 200 seeds $=\frac{7\times 200}{10}=140$

And in XY plane, seeds are taken on x axis and plants growing on y axis, its graph looks as:

Conclusion:

The different seeds are available from the set of domain, so its domain is $\{50,100,150,200\}$ and the different number of plants calculated from the set of range, so its range is $\{35,70,105,140\}$ .