 Hello and welcome to the session. In this session, we will discuss a question which says that the initial population of a city was 20,000. Later on, with each consecutive year, the population of the city increases by 1,600, write an expression for the population P as a function of number of years M, determine the rate of change and the initial value of the linear function. Now before starting the solution of this question, we should know a result. Now any linear expression is of the form y is equal to Mx plus b. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now where we are given, what is the description of the function? We are given initially the population of the city was 20,000 and with each consecutive year, it increases by 1,600. Now we have to write a linear expression for the population as a function of number of years. Now here, population is denoted by and number of years are represented by M. Now here it is increasing with years, initial dependence and number of years. Thus it is a dependent variable and number of years which are denoted by M represent dependent variable. Now the change in population is 1,600 people per year. So here, population is increasing at a range of 600 people, the population 1,600 and we have to write a linear expression for population as a function of number of years. And from the key idea, we know that any linear expression is of the form y is equal to mx plus v where x is the independent variable and y is the dependent variable. Now here is the dependent variable and also in n years, the population is increased by 1,600 and required expression p is equal to 20,000 plus 1,600 n. Now here we are putting a positive sign because population is increasing by 1,600 people per year. We can write it as p is equal to 1,600 n plus 20,000. So this is the required linear expression for the population p as a function of number of years n. Now here we have to determine the rate of change and initial value of the linear function. Now in the question it has given that initial population was 20,000. The rate of change in population is 1,600 people per year. Now the initial value 20,000 the y intersects 600 which is the slope. This equation let this be equation 1. So 1,600 is the slope of equation 1. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.