Question

Until a Labrador puppy is 30 weeks old, it gains about the same amount of weight each week. A newborn Labrador puppy weighs 2 lb.

A. Use the information shown to write a linear function describing the weight of the Labrador puppy over time. Be sure to define your variables.
B. What is the domain of this function?

Answer 1

A linear function describing the weight of a Labrador puppy as it grows can be defined as W(t) = 2 + kt, where W(t) is the weight in pounds and t is the number of weeks. The constant k represents the weekly weight gain. The domain of this function is [0, 30], representing the age range in weeks for which the weight gain is consistent.

Step-by-step explanation:

To write a linear function describing the weight of the Labrador puppy over time, let's define W(t) as the weight of the puppy at time t, where t is the number of weeks since birth. The given information tells us that at birth (t = 0), the weight of the puppy is 2 pounds. Let k be the constant amount of weight the puppy gains each week. Then, the function can be expressed as:

W(t) = 2 + kt

Since we are not given the exact value of k, we can only express the function in terms of k. To determine the domain of this function, we consider the natural constraints of the problem. The weight gain is consistent only until the puppy is 30 weeks old, so the domain is the set of all non-negative numbers less than or equal to 30. Mathematically, we can write the domain as [0, 30].

Answer 2

The linear function for the weight of a Labrador puppy as it grows can be represented as w(t) = mt + 2, where m is the constant rate of weight gain and t is the time in weeks. The domain of the function is [0, 30], including all weeks from birth up to 30 weeks old.

Step-by-step explanation:

To answer part A, let us define a linear function that describes the weight of the Labrador puppy over time. Let w(t) be the weight of the puppy in pounds at t weeks old, and let t be the time in weeks since the puppy was born. The function can be written in the form of w(t) = mt + b, where m is the constant rate of weight gain per week, and b is the initial weight of the puppy at birth. Since the puppy weighs 2 lb at birth, we have w(t) = mt + 2. However, since the exact rate of weight gain is not provided, the function remains in terms of m until we know the specific constant rate of weight gain.

For part B, the domain of this function refers to all the possible values that t can take on, that is, the age of the puppy in weeks. The puppy's age can range from 0 weeks (at birth) to 30 weeks (the age until which it gains a constant amount of weight each week). Therefore, the domain of w(t) is all real numbers between 0 and 30, inclusive. Formally, this is written as [0, 30].