Question

1. a baby elephant can weigh between 200 - 300 pounds at birth, making them the largest land - animals. the weight the baby gains daily over the first 6 months of its life can be modeled by a linear relationship. the equation y = 2x+239 models the weight in pounds, y, of a baby elephant x days after it was born.

a. how much did the baby elephant weigh at birth? explain. (2 points)
b. according to the model, how much weight does the elephant gain per day? explain (2 points)

Explanation:

Step1: Identify the linear - equation form

The linear - equation is in the form \(y = mx + b\), where \(y\) is the weight in pounds, \(x\) is the number of days after birth, \(m\) is the rate of weight gain per day, and \(b\) is the initial weight at birth. The given equation is \(y = 2x+239\).

Step2: Find the weight at birth

When \(x = 0\) (at birth), substitute \(x = 0\) into the equation \(y = 2x + 239\). Then \(y=2\times0 + 239=239\) pounds.

Step3: Find the daily weight - gain

In the linear equation \(y = mx + b\), the coefficient of \(x\) represents the slope or the rate of change. In the equation \(y = 2x+239\), the coefficient of \(x\) is \(2\). So the baby elephant gains 2 pounds per day.

Answer:

a. The baby elephant weighed 239 pounds at birth. This is found by substituting \(x = 0\) into the equation \(y = 2x + 239\) since \(x = 0\) represents the time of birth.
b. The baby elephant gains 2 pounds per day. This is because in the linear equation \(y = 2x+239\), the coefficient of \(x\) (which is 2) represents the daily rate of weight - gain.