   Chapter 9.8, Problem 43E Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Solutions

Chapter
Section Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

Average annual wage Using Social Security Administration data for selected years from 2012 and projected to 2050, the U.S. average annual wage, in thousands of dollars, can be modeled by W ( t )   =   0.0212 t 2.11 where t is the number of years past 1975.(a) Use the model to find a function that models the instantaneous rate of change of W.(b) Find a function that models the rate at which the instantaneous rate from part (a) is changing.(c) Find and interpret w(50), W'(50), and W"(50).

(a)

To determine

To calculate: The rate of change in the annual wage (in thousands of dollars) when the average annual wage is given by W(t)=0.0212t2.11.

Explanation

Given information:

The average annual wage is given by

W(t)=0.0212t2.11

where t is the number of years past 1975.

Formula used:

The power rule for differentiation states that,

ddx(xk)=kxk1

The derivative of a constant times a function is

ddx[cf(x)]=cddx(f(x))

Calculation:

Consider the equation,

W(t)=0

(b)

To determine

To calculate: The second derivative of the W(t)=0.0212t2.11 with respect to time t where t is the number of years past 1975.

(c)

To determine

The values of W(t), W(t) and W(t) at t=50 and interpret the results obtained.

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