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

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 2.7, Problem 34E

a.

To determine

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

Expert Solution

### Explanation of Solution

Given information:

P(t) is the percentage of Americans under the age 18 of at time t

The table gives values of this function in census years from 1950 to 2000

 t P(t) t P(t) 1950 31.1 1980 28.0 1960 35.7 1990 25.7 1970 34.0 2000 25.7

Calculations:

Here P'(t) shows the slope of the tangent of the curve made by the function or rate of change of Americans under the age 18 with respect to time (in years). The unit of P(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

Expert Solution

### Explanation of Solution

Given information:

P(t) is the percentage of Americans under the age 18 of at time t

The table gives values of this function in census years from 1950 to 2000

 t P(t) t P(t) 1950 31.1 1980 28.0 1960 35.7 1990 25.7 1970 34.0 2000 25.7

Calculations:

Here P'(t) shows the slope of the tangent of the curve made by the function or rate of change of Americans under the age 18 with respect to time (in years) . The unit of P(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

f'(x)=limh0f(x+h)f(x)h

 t P(t) P'(t) t P(t) P'(t) 1950 31.1 1980 28.0 -0.6 1960 35.7 0.46 1990 25.7 -0.23 1970 34.0 -0.17 2000 25.7 0

c.

To determine

Expert Solution

### Explanation of Solution

Given information:

P(t) is the percentage of Americans under the age 18 of at time t

The table gives values of this function in census years from 1950 to 2000

 t P(t) t P(t) 1950 31.1 1980 28.0 1960 35.7 1990 25.7 1970 34.0 2000 25.7

Calculations:

Here P'(t) shows the slope of the tangent of the curve made by the function or rate of change of Americans under the age 18 with respect to time (in years) . The unit of P(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

f'(x)=limh0f(x+h)f(x)h

 t P(t) P'(t) t P(t) P'(t) 1950 31.1 1980 28.0 -0.6 1960 35.7 0.46 1990 25.7 -0.23 1970 34.0 -0.17 2000 25.7 0

The graph of P(t) is shown below.

The graph of P'(t) is shown below.

d.

To determine

Expert Solution

### Explanation of Solution

Given information:

P(t) is the percentage of Americans under the age 18 of at time t

The table gives values of this function in census years from 1950 to 2000

 t P(t) t P(t) 1950 31.1 1980 28.0 1960 35.7 1990 25.7 1970 34.0 2000 25.7

Calculations:

Here P'(t) shows the slope of the tangent of the curve made by the function or rate of change of Americans under the age 18 with respect to time (in years) . The unit of P(t) will be Unemployed peer year.

The slope of the tangent is given the formula,

f'(x)=limh0f(x+h)f(x)h

The value of P'(t) can be more accurate if the time interval is less and more values of P(t) is obtained.

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!