BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.7, Problem 33E

a.

To determine

The meaning of U'(t) and also the unit of U'(t) .

Expert Solution

Explanation of Solution

Given information:

The unemployment rate U(t) varies with time.

The table gives the percentage of unemployed in US labor force from 1998 to 2007

    tU(t)tU(t)
    19984.520036.0
    19994.220045.5
    20004.020055.1
    20014.720064.6
    20025.820074.6

Calculations:

Here U'(t) shows the slope of the tangent of the curve made by the function or rate of change of unemployed with respect to time (in years) . The unit of U'(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

  f'(x)=limh0f(x+h)f(x)h

b.

To determine

The estimated values of U'(t) in a tabulated manner.

Expert Solution

Explanation of Solution

Given information:

The unemployment rate U(t) varies with time.

The table gives the percentage of unemployed in US labor force from 1998 to 2007

    tU(t)tU(t)
    19984.520036.0
    19994.220045.5
    20004.020055.1
    20014.720064.6
    20025.820074.6

Calculations:

Here U'(t) shows the slope of the tangent of the curve made by the function or rate of change of unemployed with respect to time (in years) . The unit of U'(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

  f'(x)=limh0f(x+h)f(x)h

    tU(t)U'(t)tU(t)
    19984.520036.00.2
    19994.2-0.320045.5-0.5
    20004.0-0.220055.1-0.4
    20014.70.720064.6-0.5
    20025.81.120074.60

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