SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
Part A:
The horizontal asymptote of the function is given as follows:
[tex]\begin{gathered} \text{ C= }\frac{3t^2\text{ + t}}{t^3+50} \\ C\text{ =}\frac{t^2\text{ (3+}\frac{1}{t})}{t^{3\text{ }}(1+\frac{50}{t^3})} \\ as\text{ t}\rightarrow0,\text{ C}\rightarrow0 \\ So,\text{ the horizontal asymptote: y = 0} \end{gathered}[/tex]
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:
[tex]\begin{gathered} t\text{ = 4.486 seconds} \\ t\text{ }\approx\text{ 4. 5 seconds ( 1 decimal place)} \end{gathered}[/tex]
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:
[tex]\begin{gathered} t\text{ < 2.645 seconds} \\ t\text{ < 2.6 seconds ( 1 decimal place)} \end{gathered}[/tex]
