Question

1174. Before reading any further, look back at the handoutIdentifying and interpreting Rate of Change from class.Find the function that examined how well a medicineproduced antibodies in a patient.Data for Medicine BDays PassedImagine that the same scientist tested a second medicine(Medicine B) and recorded the data in the table at theright after following a patient for several days.0Antibodies in theSample of Blood6090120123150a. How many days would it take for the patient's bloodsample to have 480 antibodies? Show how youcalculated your answer.418052106240b. What is the rate of change for this function? How can it be interpreted in terms of the contextof the problem?c. If you were ill and you had both Medicine B and Medicine A (from the problem you did inclass) to choose from, which would you prefer? Why?

Answer 1

Given a table represents a relation between days passed and the antibodies in the sample of blood

The table represents a linear relation

Let the number of days = d

And the antibodies in the sample of blood = A

So,

$A=m\cdot d+c$

When d = 0, A = 60

So, c = 60

When d = 1, A = 90

So,

$\begin{gathered} 90=m+60 \\ m=90-60=30 \end{gathered}$

So, the relation will be:

$A=30d+60$

a. How many days would it take for the patient's blood sample to have 480 antibodies?

So, A= 480

Substitute with A into the equation then solve for d

$\begin{gathered} 480=30d+60 \\ 30d=480-60 \\ 30d=420 \\ d=\frac{420}{30}=14 \end{gathered}$

So, the number of days = 14

b. What is the rate of change for this function?

The rate of change = m = 30

which every day the antibodies increases by 30 per day