Chapter 9.7, Problem 26PPS

To determine

Whether the given situation represents linear or non-linear function

Answer to Problem 26PPS

The situation represents a non-linear function

Explanation of Solution

Given:

The population of the city increases by 3% each year

Calculation:

Let the population of the city for I year is ‘x’.

Population of the city in II year will be $\left(x+0.03x\right)$

Similarly, the population of the city in III year will be

  $\left(x+0.03x\right)+0.03\left(x+0.03x\right)$

And so on.

Linear Functions: The graph of linear functions is always a straight line. These functions have the form $y=a+bx$ .

The slope of the linear graph always remains constant. The slope of the equation is given by:

  $m=\frac{y_2-y_1}{x_2-x_1}$

From the above analysis, we can see that slope of the given data will keep on changing.

Hence, the given data represents anon-linear function.