Chapter 9.8, Problem 44E

### 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

# Demographics The makeup of various groups within the U.S. population may reshape the electorate in ways that could change political representation and policies. By using U.S. Department of Labor data from 1980 and projected to 2050 for the civilian non-institutional population ages 16 or older, in millions, the population of those who are non-White or Hispanic can be modeled by the function P ( t )   = 0.707 t 11.17 +   20.0 where t is the number of years past 1970.(a) Find the function that models the instantaneous rate of change of the population of non-Whites or Hispanics.(b) Find the function that models how fast the rate found in part (a) changes.(c) Find and interpret P(55), P'(55), and P"(55).

(a)

To determine

To calculate: The function of the instantaneous rate of change of the population of non-whites or Hispanic if the function of population is given as P(t)=0.707t1.17+20.0.

Explanation

Given Information:

The function of population of non-whites or Hispanic is given as,

P(t)=0.707t1.17+20.0

Where, t is the number of years starting from 1970.

Formula used:

The power rule of differentiation,

ddx(xn)=nxnâˆ’1

Where, n is any real number.

The constant rule for differentiation,

ddx(cf(x))=cfâ€²(x)

Where, c is a constant.

Calculation:

Consider the function of population,

P(t)=0.707t1.17+20.0

Differentiate the function with respect to t,

Pâ€²(t)=ddt(0

(b)

To determine

To calculate: The function that gives the speed at which the rate of the function P(t)=0.827t0.17 changes.

(c)

To determine

To calculate: The value of P(55),P(55) and P(55) and interpret the result.

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