A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day – SAT Math Prep
A model predicts that a certain animal weighed 241 pounds when it was born and that the animal gained 3 pounds per day in its first year of life. This model is defined by an equation in the form f(x) = a + bx, where f(x) is the predicted weight, in pounds, of the animal x days after it was born, and a and b are constants. What is the value of a?
Answer
The equation we have to solve is f(x) = a + bx
Here, f(x) is the ‘predicted weight’ after x days, and a in a constant.
The question also says each day the weight increases by 3, which means 3 is the slope (gradient) of the linear equation. After 1 day, the weight is 3(1) = 3 pounds, after 2 days, it is 3(2) = 3 pounds, and so on. Therefore, in the linear equation, above, we can write f(x) = a + 3x
The question provides the following data:
Newborn weight (at 0 days) = 241 pounds
Let’s add this to the equation, where x = 0 days
f(x) = a + bx
241 = a + 3(0)
a = 241 = constant.
The value of a = 241
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