Answer :
To solve the problem, we need to find the value of [tex]\( a \)[/tex] in the equation [tex]\( f(x) = a + b \cdot x \)[/tex], which represents the predicted weight of an animal [tex]\( x \)[/tex] days after it was born.
Here's the step-by-step breakdown:
1. Understanding the Equation: The equation [tex]\( f(x) = a + b \cdot x \)[/tex] is a linear equation where:
- [tex]\( f(x) \)[/tex] is the predicted weight of the animal in pounds.
- [tex]\( a \)[/tex] is the initial weight of the animal when it was born.
- [tex]\( b \)[/tex] represents the rate of weight gain per day.
- [tex]\( x \)[/tex] is the number of days after the animal was born.
2. Identify the Constants from the Problem:
- We are given that the animal weighed 241 pounds when it was born. This is the initial weight, which corresponds to the constant [tex]\( a \)[/tex] in the equation.
- The animal gains 3 pounds per day, which is the rate of change [tex]\( b \)[/tex] in the equation.
3. Conclusion: Since [tex]\( a \)[/tex] represents the initial weight of the animal when it was born, and we know from the information given that this weight is 241 pounds, the value of [tex]\( a \)[/tex] is 241.
Thus, the correct answer for the value of [tex]\( a \)[/tex] is A) 241.
Here's the step-by-step breakdown:
1. Understanding the Equation: The equation [tex]\( f(x) = a + b \cdot x \)[/tex] is a linear equation where:
- [tex]\( f(x) \)[/tex] is the predicted weight of the animal in pounds.
- [tex]\( a \)[/tex] is the initial weight of the animal when it was born.
- [tex]\( b \)[/tex] represents the rate of weight gain per day.
- [tex]\( x \)[/tex] is the number of days after the animal was born.
2. Identify the Constants from the Problem:
- We are given that the animal weighed 241 pounds when it was born. This is the initial weight, which corresponds to the constant [tex]\( a \)[/tex] in the equation.
- The animal gains 3 pounds per day, which is the rate of change [tex]\( b \)[/tex] in the equation.
3. Conclusion: Since [tex]\( a \)[/tex] represents the initial weight of the animal when it was born, and we know from the information given that this weight is 241 pounds, the value of [tex]\( a \)[/tex] is 241.
Thus, the correct answer for the value of [tex]\( a \)[/tex] is A) 241.
