Question

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}f(x)=−1.25⋅ln( x 1 ​ )f, left parenthesis, x, right parenthesis, equals, minus, 1, point, 25, dot, natural log, left parenthesis, start fraction, 1, divided by, x, end fraction, right parenthesis, where xxx is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)g(x)=−1.8⋅ln( x 2.1 ​ )g, left parenthesis, x, right parenthesis, equals, minus, 1, point, 8, dot, natural log, left parenthesis, start fraction, 2, point, 1, divided by, x, end fraction, right parenthesis. Here are the graphs of

Answer 1

The amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

How to compare both functions?

The functions are given as:

$f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}$

$g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)$

Next, we represent both functions on a graph.

From the attached graph, we can see that both functions intersect at (11.34, 3.04)

This means that the amount of medication that stays in the bloodstream is the same at 3.04 hours for the two medications

Read more about functions at:

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Complete question

A pharmaceutical scientist studying two medications wonders how long different amounts of each medicine stay in someone's bloodstream. The amount of time (in hours) one medication stays in the bloodstream can be modeled by $f(x)=-1.25\cdot \ln{\left(\dfrac{1}{x}\right)}$ where x is the initial amount of the medicine (in milligrams). The corresponding function for the other medication is $g(x)=-1.8\cdot\ln\left(\dfrac{2.1}{x}\right)$. Here are the graphs of