For a function value in a real-world model, the number in parentheses is the input, and the function gives an output. Match each number to the quantities and units in the prompt. You can check a stated approximation by defining and evaluating the function in Desmos. The tempting trap is to treat an amount remaining as a percent or an amount lost.
Hints
- Hint 1
The number inside a function’s parentheses is its input. Here, the input measures hours since noon. What time does the input refer to?
- Hint 2
A function’s output takes its units from the quantity the function models, not from its input. Which words in the prompt tell you the units of ?
Step-by-step
Read the input, then the output
Step 1Identify what the input means
In , the is the input. The problem says measures hours after noon, so describes the tracer 6 hours after noon. The doesn’t describe a rate or an amount lost.
- Step 2
Evaluate and interpret the output
Type , then type on the next line to evaluate the function. Desmos shows about , which agrees with the stated approximation of . The output keeps the units and meaning assigned to . So about milligrams of tracer remain in the body hours after noon. Choice C.