Final answer:
The equation that models the total cost as a function of the number of T-shirts ordered is C = 12t + 25, where 'C' is the total cost and 't' is the number of T-shirts. The initial value is $25, representing the shipping cost, and the rate of change is $12, representing the cost per T-shirt.
Step-by-step explanation:
The question involves finding the total cost of T-shirts as a function of the number of shirts ordered. The given school paid $1,825 for 150 shirts, which includes a $25 flat-rate shipping cost. To find the cost per shirt minus the shipping cost, we subtract the shipping cost from the total cost and then divide by the number of shirts: (Total cost - Shipping cost) / Number of shirts = (1825 - 25) / 150 = 1800 / 150 = $12 per shirt.
Therefore, the equation that models the total cost (C) as a function of the number of T-shirts (t) ordered is C = 12t + 25. Here, 'C' represents the total cost, 't' represents the number of T-shirts ordered, '12' is the cost per T-shirt, and '25' is the flat-rate shipping cost.
The initial value of the function is $25, which represents the flat-rate shipping cost. The rate of change of the function is $12, representing the cost of each additional T-shirt.