A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.

The amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \cdot \ln \left(\frac{1}{x}\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.

Which statements represent the meaning of the intersection point of the graphs?
Choose all answers that apply:
A It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \mathrm{mg}$.
B It gives the solution to the equation $-1.25 \cdot \ln \left(\frac{1}{x}\right)=4$.
c. It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.
D It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.

Question

A pharmaceutical scientist making a new medication wonders how much of the active ingredient to include in a dose. They are curious how long different amounts of the active ingredient will stay in someone's bloodstream.

The amount of time (in hours) the active ingredient remains in the bloodstream can be modeled by $f(x)=-1.25 \cdot \ln \left(\frac{1}{x}\right)$, where $x$ is the initial amount of the active ingredient (in milligrams). Here is the graph of $f$ and the graph of the line $y=4$.

Which statements represent the meaning of the intersection point of the graphs?
Choose all answers that apply:
A It describes the amount of time the active ingredient stays in the bloodstream if the initial amount of the active ingredient is $4 \mathrm{mg}$.
B It gives the solution to the equation $-1.25 \cdot \ln \left(\frac{1}{x}\right)=4$.
c. It describes the situation where the initial amount of the active ingredient is equal to how long it stays in the bloodstream.
D It gives the initial amount of the active ingredient such that the last of the active ingredient leaves the bloodstream after 4 hours.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the intersection point of the graphs of $f(x)=-1.25 \cdot \ln \left(\frac{1}{x}\right)$ and $y=4$, we set $f(x)$ equal to 4. ‖ ‖ step 2 ⋮ Solve the equation $-1.25 \cdot \ln \left(\frac{1}{x}\right) = 4$. ‖ ‖ step 3 ⋮ Using the asksia-ll calculation, the solution to the equation is $x = e^{\frac{16}{5}}$. ‖ ∻[question number] Answer∻ ***B*** ∻Key Concept∻ ⚹Intersection of Graphs⚹ ∻Explanation∻ ⚹The intersection point of the graphs of two functions represents the x-value(s) for which the functions have the same y-value. In this context, it represents the initial amount of the active ingredient such that the time it stays in the bloodstream is 4 hours.⚹◊What is the equation representing the amount of time the active ingredient stays in the bloodstream based on the given information?⍭ Generate me a similar question◊

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