Question

5) The concentration of C of a chemical in the bloodstream t hours after injection into themuscle tissue is given byC= (3t^2+ t) / (t^3 + 50) t >= 0A) Determine the horizontal asymptote of the function and interpret its meaning in context ofthe problem.B) Use your graphing calc to sketch the function (note the scale[0,10]x[0,1]) then approximate the time when the concentration is a maximum.C) When is the concentration less than 0.345?Pls refer to pic for details

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

Part A:

The horizontal asymptote of the function is given as follows:

`\begin{gathered} \text{ C= }\frac{3t^2\text{ + t}}{t^3+50} \\ C\text{ =}\frac{t^2\text{ (3+}(1)/(t))}{t^{3\text{ }}(1+(50)/(t^3))} \\ as\text{ t}\rightarrow0,\text{ C}\rightarrow0 \\ So,\text{ the horizontal asymptote: y = 0} \end{gathered}`

Part B:

With the use of the graphical calculator, the approximate time when the concentration is a maximum is:

From the graph, the approximate time when the concentration is a maximum is at:

`\begin{gathered} t\text{ = 4.486 seconds} \\ t\text{ }\approx\text{ 4. 5 seconds ( 1 decimal place)} \end{gathered}`

Part C:

When is the concentration less than 0.345?

From the graph, the value of t when the concentration is less than 0.345 is at:

`\begin{gathered} t\text{ < 2.645 seconds} \\ t\text{ < 2.6 seconds ( 1 decimal place)} \end{gathered}`