Note: The item below has been reviewed and is scheduled to be updated. All students will receive full credit for any response to the following.
The total cost for a business to make greeting cards can be divided into one-time costs (e.g., a printing machine) and repeated costs (e.g., ink and paper). Suppose that the one-time cost to be able to make cards is $300, the total cost to make 300 cards is $900.00, and the total cost to make 650 cards is $1,600.00. What is the total cost to make 1,000 cards? Find the function rule to help you solve the problem.
Number of Cards Total Cost
0 $300
300 $900
650 $1,600
1,000
A. $2,100.00
B. $2,300.00
C. $2,500.00
D. $3,000.00
To find the function rule, we need to determine the repeated cost per card. We can use the two data points we have:
- For 300 cards, the total cost is $900. This means the repeated cost per card is (900-300)/300 = $2.
- For 650 cards, the total cost is $1600. This means the repeated cost per card is (1600-300)/350 = $3.14.
We can then assume that the repeated cost per card is a linear function of the number of cards, and use these two data points to find the equation of the line:
slope = (3.14-2)/(650-300) = 0.004
y-intercept = 2 - 0.004*300 = 0.8
So the function rule is:
repeated cost per card = 0.004 * number of cards + 0.8
To find the total cost for 1000 cards, we simply plug in 1000 for the number of cards:
total cost = one-time cost + repeated cost per card * number of cards
total cost = 300 + (0.004*1000 + 0.8)*1000
total cost = $2,500.
Therefore, the answer is (C) $2,500.00.