Question

a die is used in the blood to measure a patient's cardiac output when there's potential for a heart attack.in A Normal Heart the concentration of the dye is modeled by the function...

Answer 1

a) Here, we want to use a graphing software to find the zeros of the given function

A graph of the equation is shown below;

What is next is to find the roots

As the function is quartic, it is expected that we have four roots

However, the question asks us for real roots only

According to the graph, the real roots are the points at which the plot crosses the x-axis

We have the points at (0,0) and (27.897,0)

b) What must be true of two of the zeros of of this function is that they are complex while the other two are real (a total of 4 zeros)

c) Lastly, we want to explain why the end behavior of the plot makes sense based on the leading coefficient and degree

As we can see from the function, since it is quartic, the degree is even

Also, as we can see, the leading coeffiecient of the function is negative

Thus, the expected end behavior is that as follows;

`\begin{gathered} c(t)\text{ }\rightarrow\text{ -}\infty\text{ as t }\rightarrow\text{ -}\infty \\ c(t)\rightarrow\text{ -}\infty\text{ as t }\rightarrow\text{ }\infty \end{gathered}`

Hence, from above, it is expected that the end behavior is towards negative infinity as the value of t tends toward positive and negative infinity

From the plot, we can see that this is obeyed and thus we can deduce that the plot actually follows the theoretical expectation