Question

# You have an ant form with 22 ants. The population of ants in your farm doubles every 3 months.

a) Complete the table .

b) Is the relation forms a function ? If so , is it a linear function or non linear function ? Explain.

Hint:

### First, we derive an equation to represent the relationship between the ant population with respect to the number of months. We use the slope intercept form of an equation to derive this relationship. We complete the table with the help o this equation. Next, we check if it is a function and if it is linear. An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x and a function is linear if it has a constant slope.

## The correct answer is: 2, 6 and 8

*Step by step solution:*

Given,

Population of the ant farm initially = 22

The population doubles every 3 months.

Rate at which the population of the ant farm increases per month =

We know, the slope intercept form of the equation is y = mx + c, where m is the slope and c is the y intercept.

Here, m = = 1.5 and c=22

Thus, the equation representing the relationship between the ant population with respect to the number of months is

y = 1.5x + 22

We use this equation to complete the table.

We can see that for x = 0, we get y = 22

Putting x = 3 in the above equation, we get

y = 1.5 3 + 22 = 4.5 + 22 = 26.5

Similarly, putting in the above equation, we get

y = 15 6 + 22 = 9 + 22 = 31

Finally, putting in the above equation, we have

y = 1.5 9 + 22 = 13.5 + 22 = 35.5

Putting these values in the table, we have

No. of months (x)

0

3

6

9

Ant population (y)

22

26.5

31

35.5

The above relation forms a function as there is a unique value of y for every value of x.

It is also a linear function as the rate of change of ant population or the slope of the equation is a constant value 1.5.

We can also check if the relation is a function or not graphically by using the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point.

And it is linear if the graph drawn is a straight line.

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b) Graph the function and tell whether it is a linear function or non linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

### A train leaves the station at time . Travelling at a constant speed, the train travels 360 kilometers in 3 hours.

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b) Graph the function and tell whether it is a linear function or non linear function.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.

### Do the ordered pairs plotted in the graph below represents a function? Explain.

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### Do the ordered pairs plotted in the graph below represents a function? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### The relationship between the number of hexagons, , and the perimeter of the figure they form, , shown in the graph. Is the perimeter of the figure a function of the number of hexagons? Explain.

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