Final answer:
The total cost function represents a fixed cost plus a variable cost based on time, with a specific condition for the time values.
Step-by-step explanation:
The total cost function represents the overall cost incurred by a business or individual to produce a certain quantity of goods or provide a specific service. It is a mathematical model that relates the total cost to the quantity produced or some other relevant variable.
The general form of a total cost function is often denoted as C(q)C(q), where CC represents the total cost and qq is the quantity of goods or services produced.
The given function is: c(t) = 100 + 50(t-3)
To understand this equation, let's break it down:
The constant term 100 represents a fixed cost or initial cost.
The term 50(t-3) represents the variable cost, where t represents the time in hours. By subtracting 3 from t, it ensures that the function is only valid for t values greater than 3.
So, the total cost (c) is equal to the fixed cost (100) plus the variable cost (50 times the difference between t and 3).