   Chapter 2.7, Problem 50E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The table shows values of the viral load V(r) in HIV patient 303, measured in RNA copies/mL, t days after ABT-538 treatment was begun. T 4 8 11 15 22 V(t) 53 18 9.4 5.2 3.6 (a) Find the average rate of change of V with respect to t over each time interval:(i) [4, 11](ii) [8, II](iii) [11, 15](iv) [11, 22]What are the units?(b) Estimate and interpret the value of the derivative V' (11).

(a)

To determine

To find: The average rate of change of V(t) over each time interval.

Explanation

Given:

Let V(t) represents viral load in HIV patient with respect to time t.

The time t is measured in days and V(t) is measured in RNA copies/mL.

Formula used:

The average rate of change of V with respect to t on the interval [t1,t2] is,

ΔVΔt=V(t2)V(t1)t2t1 (1)

Calculation:

Section (i)

Obtain the average rate of change of V(t) on the interval [4,11].

Substitute 4 for t1 and 11 for t2 in equation (1),

ΔVΔt=V(11)V(4)114

Consider the given table, the values of V(4)=53 and V(11)=9.4.

ΔVΔt=9.453114=43.67=6.228576.23

Thus, the average rate of change of V(t) on the interval [4,11] is 6.23 RNA copies/mLday_.

Section (ii)

Obtain the average rate of change of V(t) on the interval [8,11].

Substitute 8 for t1 and 11 for t2 in equation (1),

ΔVΔt=V(11)V(8)118

Consider the given table, the values of V(8)=18 and V(11)=9.4.

ΔVΔt=9.418118=8.63=2.866¯2

(b)

To determine

To estimate: The derivative of a function V(t) at t=11 and state the interpretation.

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