Question

3.5 relations and functions (homework)
score: 15/16 answered: 15/16
question 16
the daily cost to a manufacturing company is modeled by the function ( c(x) = 5x + 1200 ) where ( c(x) ) is the total daily cost and ( x ) is the number of items manufactured. find ( c(8000) ), and interpret its meaning.
( c(8000) = )
this value represents
○ the number of items manufactured when the daily cost is 8000
○ the daily cost when 8000 items are manufactured
○ the product of the daily cost and the number of items

Explanation:

Step1: Substitute x = 8000 into the function

We have the cost function \( C(x) = 5x + 1200 \). To find \( C(8000) \), we substitute \( x = 8000 \) into the function. So we get \( C(8000)=5\times8000 + 1200 \).

Step2: Calculate the value

First, calculate \( 5\times8000 = 40000 \). Then add 1200 to it: \( 40000+1200 = 41200 \).

For the interpretation, since \( C(x) \) is the total daily cost and \( x \) is the number of items manufactured, \( C(8000) \) represents the daily cost when 8000 items are manufactured.

Answer:

\( C(8000)=\boldsymbol{41200} \)

This value represents: The daily cost when 8000 items are manufactured