   Chapter 9.6, Problem 50E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Data entry speed The data entry speed (in entries per minute) of a data clerk trainee is S = 10 0.8 x + 4 ,  0 ≤ x ≤  100 where x is the number of hours of training he has had. What is the rate at which his speed is changing, and what does this rate mean when he has had(a) 15 hours of training?(b) 40 hours of training?

(a)

To determine

To calculate: The rate at which the speed of the clerk trainee is changing. Interpret the rate when he has had 15 hours of training. The data entry speed (in entries per minute) of a data clerk trainee is S=100.8x+4, 0x100, where x is the number of hours of training he has had.

Explanation

Given Information:

The data entry speed (in entries per minute) of a data clerk trainee is S=100.8x+4, 0x100, where x is the number of hours of training he has had.

Formula used:

The power rule of differentiation,

ddxxn=nxn1

Calculation:

Consider the provided function,

S=100.8x+4

Consider (0.8x+4) to be u,

S=10u=10(u)1/2

Differentiate both sides with respect to x,

dSdx=ddx(10u1/2)

Simplify using the power rule,

dSdx=ddx(10u1/2)=10(12)u121dudx=5u1/2dudx

Substitute (0.8x+4) for u,

dSdx=5(0.8x+4)1/2ddx(0

(b)

To determine

To calculate: The rate at which the speed of the clerk trainee is changing. Interpret the rate when he has had 40 hours of training. The data entry speed (in entries per minute) of a data clerk trainee is S=100.8x+4, 0x100, where x is the number of hours of training he has had.

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