Maths-
General
Easy

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:

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

### Step by step solution:Given,Population of the ant farm initially = 22The 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=22Thus, the equation representing the relationship between the ant population with respect to the number of months isy = 1.5x + 22We use this equation to complete the table.We can see that for x = 0, we get y = 22Putting x = 3 in the above equation, we gety = 1.5 3 + 22 = 4.5 + 22 = 26.5Similarly, putting  in the above equation, we gety = 15  6 + 22 = 9 + 22 = 31Finally, putting  in the above equation, we havey = 1.5  9 + 22 = 13.5 + 22 = 35.5Putting 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.