Chapter 9.8, Problem 43E

### Mathematical Applications for the ...

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

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)=kxkâˆ’1

The derivative of a constant times a function is

ddx[câ‹…f(x)]=câ‹…ddx(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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