To find the function rule, we need to determine the relationship between the number of cards and the total cost. We can start by finding the difference in total cost and number of cards between two data points:
- To make 350 more cards (from 300 to 650), the total cost increased by $700 ($1600 - $900).
- This means that the cost per card for the repeated costs is $2 ($700 / 350).
Using this cost per card, we can calculate the total cost for 1000 cards:
- To make 350 more cards (from 650 to 1000), the total cost will increase by $700 ($2 x 350).
- Therefore, the total cost to make 1000 cards is $2300 ($1600 + $700).
So the function rule is:
Total cost = one-time cost + (cost per card x number of cards)
Plugging in the values we have:
Total cost = $300 + ($2 x number of cards)
Therefore, the total cost to make 1,000 cards is $2,300.00.
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.
(1 point)
Number of Cards Total Cost
0 $300
300 $900
650 $1,600
1,000
$2,100.00 $2,300.00 $2,500.00 $3,000.00
1 answer