Ask yourself: Is the same number of units of medication lost every hour, or is the same percentage of whatever is currently there lost every hour?

Think about a situation where, each hour, you multiply the current amount by the same number (like $0.85$) again and again. What general kind of function has the variable (time) in the exponent like that?

Pick a simple starting amount, such as 100 units. In Desmos, enter

• y1 = 100*(0.85^x)

This represents losing 15% each hour (multiplying by $0.85$ every hour). Look at how the graph behaves as $x$ (time) increases: the curve goes downward and gradually flattens out.

Now enter a model that loses a fixed amount each hour, for example:

• y2 = 100 - 15x

This graph is a straight line slanting down. Notice that here you lose exactly 15 units every hour, not 15% of the current amount. Compare this straight line to the curved graph from step 1 and observe which better matches a repeated percent loss.

For contrast, enter two increasing models:

• y3 = 100 + 15x (increasing linear)
• y4 = 100*(1.15^x) (percent increase each hour)

Both of these graphs rise as $x$ increases, while the situation in the problem clearly describes the amount going down. On the SAT, choose the option that names the type of function whose graph matches the downward curve created by repeatedly multiplying by $0.85$ each hour.

The problem says 15% of the amount present is lost every hour.

If part of the medication is being lost, the total amount in the bloodstream is going down as time goes on, not up. So the relationship between amount and time must be decreasing, not increasing.

Losing 15% of the current amount each hour means you keep 85% of the current amount each hour, because $100\%-15\%=85\%$.

• If the amount at some hour is $A$, then after 1 more hour the amount is $0.85A$.
• After another hour, you again keep 85% of what you have then, so you multiply by $0.85$ again.

So each hour you are multiplying by the same factor, $0.85$.

Let $A_0$ be the initial amount of medication (at time $t=0$ hours).

• After 1 hour: $A_1 = A_0\cdot 0.85$.
• After 2 hours: $A_2 = A_0\cdot 0.85\cdot 0.85 = A_0\cdot 0.85^2$.
• After $t$ hours: $A(t) = A_0\cdot 0.85^t$.

Notice that time $t$ is in the exponent, and the base $0.85$ is less than 1, so the function curves downward (the amount drops quickly at first, then more slowly), not in a straight line.

Now compare with the answer choices:

• A linear function would change by the same amount (like "10 mg every hour"), giving a straight-line graph. Our model changes by the same percentage, not the same amount, and uses a power $0.85^t$, so it is not linear.
• The relationship is clearly decreasing, so any increasing option is wrong.

That means the function type that fits a repeated 15% loss each hour is a decreasing exponential function.

Correct answer: Decreasing exponential.