32. The weight of a female elephant changes at a steady rate from 1 to 3 years of age .At 1 year of age, the elephant weighed approximately 332 Ib At 3 years of age, the elephant weighed approximately 826 Ib.

## Step 1<br />The problem involves the concept of linear growth, which is a common topic in algebra. The weight of the elephant is changing at a constant rate, which means the weight gain per year is the same each year. This is a linear relationship, which can be represented by the equation \(y = mx + b\), where \(y\) is the weight of the elephant, \(x\) is the age of the elephant, \(m\) is the rate of weight gain per year, and \(b\) is the initial weight of the elephant.<br /><br />## Step 2<br />We are given two points on the line: (1, 332) and (3, 826). These points represent the age of the elephant (in years) and its weight (in pounds). We can use these points to find the slope of the line, which is the rate of weight gain per year. The slope \(m\) is calculated as the change in weight divided by the change in age, which is \((826 - 332) / (3 - 1) = 247\).<br /><br />## Step 3<br />The initial weight of the elephant, or the y-intercept \(b\), weight of the elephant at age 1, which is 332 pounds.<br /><br />## Step 4<br />So, the equation of the line that represents the weight of the elephant as a function of its age is \(y = 247x + 332\).