To determine which function represents the average manufacturing cost [tex]\(A(b)\)[/tex] in terms of the number of cars manufactured [tex]\(b\)[/tex], we need to understand the relationship between the total cost and the average cost.
The total daily cost of manufacturing [tex]\(b\)[/tex] scented candles is given by the function:
[tex]\[ C(b) = 250 + 3b \][/tex]
The average manufacturing cost [tex]\(A(b)\)[/tex] is defined as the total cost divided by the number of units [tex]\(b\)[/tex]. Mathematically, this is expressed as:
[tex]\[ A(b) = \frac{C(b)}{b} \][/tex]
Plugging the given total cost function into this formula, we get:
[tex]\[ A(b) = \frac{250 + 3b}{b} \][/tex]
Thus, the function that represents the average manufacturing cost [tex]\(A(b)\)[/tex] in terms of [tex]\(b\)[/tex] is:
[tex]\[ A(b) = \frac{250 + 3b}{b} \][/tex]
Among the provided options, the correct one is:
B. [tex]\( A(b) = \frac{250 + 3b}{b} \)[/tex]
