Question 88·Easy·Nonlinear Functions
The function models the concentration, in milligrams per liter, of a certain medicine in a patient’s bloodstream, where is the number of hours since the medicine was administered. According to the model, what is the best interpretation of the statement " is approximately equal to "? Powеrеd by Anікo
For function-interpretation questions, first underline what the input variable represents (with units) and what the function output represents (with units). When you see a notation like , label 4 as the input (for example, time) and as the output (for example, concentration), then restate it in a full sentence. Finally, eliminate choices that swap input and output, use the wrong time (like instead of the given value), or treat a single function value as a constant rate of change.
Hints
Match input and output to context
Look back at the definition of . What does stand for, and what does stand for in words and units? ЅАT prеp bу Аniko.аi
Focus on the notation
When you see , is the 4 the input (time) or the output (concentration)? What real-world quantity does represent here?
Connect the approximate value to units
If is approximately , what does measure (hours or milligrams per liter)? Which choice correctly pairs the 4 with time and the 1.67 with concentration?
Desmos Guide
Enter the function
In a Desmos expression line, type C(t) = 3.2*(0.85)^t (or just 3.2*(0.85)^t). Desmos will graph the function showing concentration versus time.
Evaluate the function at 4 hours
In a new line, type C(4) or 3.2*(0.85)^4. Desmos will display a numerical value; this is the concentration when .
Translate the Desmos output into words
Use the problem statement (where is hours since the medicine was given and is concentration in mg/L) to turn the result of C(4) into a sentence of the form: “__ hours after the medicine was administered, the concentration was approximately __ milligrams per liter,” and choose the option that matches that wording. From аnikο.aі
Step-by-step Explanation
Identify what the variables represent
From the problem, is the number of hours since the medicine was administered, and is the concentration of the medicine in the bloodstream, measured in milligrams per liter.
So:
- Input : time (hours since dose)
- Output : concentration (mg/L) at that time
Understand what means
The notation means “the value of the concentration function when .”
Because is hours since the medicine was given, corresponds to the time 4 hours after the medicine was administered. The quantity is the concentration in the bloodstream at that time.
Interpret the statement in words
The statement says that when hours, the concentration is approximately milligrams per liter.
In words: 4 hours after the medicine was administered, the concentration of the medicine in the bloodstream was approximately 1.67 milligrams per liter. This matches answer choice B.