Question 841·Easy·Math

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The function $C(t) = 3.2(0.85)^t$ models the concentration, in milligrams per liter, of a certain medicine in a patient’s bloodstream, where $t$ is the number of hours since the medicine was administered. According to the model, what is the best interpretation of the statement " $C(4)$ is approximately equal to $1.67$ "?

In a word problem, function notation pairs an input with an output: the number in parentheses is the input, and the function value is the output. Read what each represents and keep its units attached. You can define the function in Desmos and evaluate it to check a stated value. Don't swap the input and output or mistake an output for a per-hour change.

Hints

Hint 1
The input is the number inside the parentheses. In $C(4)$ , what does $4$ measure according to the definition of $t$ ? Keep that unit with the number.
Hint 2
The output is what the function returns. The problem gives the units of $C(t)$ separately from the units of $t$ . What units belong to a value of $C(t)$ ?

Step-by-step

Read the input and output
Step 1
Identify the time
The input is the number inside the parentheses. In $C(4)$ , the input is $t=4$ . Since $t$ counts hours since the medicine was administered, this means 4 hours after administration, not $1.67$ hours after.
Step 2
Identify the output's units
$C(t)$ models concentration in milligrams per liter, so its output has those units. One output gives the concentration at a particular time; it doesn't say how much the concentration changes each hour.
Step 3
Check and interpret the value
Type $C(t)=3.2(0.85)^t$ , then $C(4)$ in Desmos. It shows $1.67042$ , so the concentration is approximately $1.67$ milligrams per liter 4 hours after the medicine was administered. Choice B.

Question 841·Easy·Math

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