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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Population Growth The population P (in millions) of Brazil from 1990 through 2013 can be modeled by

P   = 0.021 t 2 + 2.77 t + 148.9 where t represents the year, with t = 0 corresponding to 1990. (Source: U.S. Census Bureau)

(a) Evaluate P for t = 0, 4, 8, 12, 16, 20, and 23. Explain these values.

(b) Find dP/dt and explain its meaning in this situation.

(c) Evaluate dP/dt for the same values as in part (a). Explain your results.

(a)

To determine

To calculate: The value of P for t=0,4,8,12,16,20 and 23 and also the meaning of each of these values, where P (in thousands) is the population of Brazil from 1990 through 2013 modeled by the equation P=0.021t2+2.77t+148.9.

Explanation

Given Information:

It is given that P (in thousands) is the population of Australia from 1990 through 2013 modeled by the equation P=0.021t2+2.77t+148.9, where t is the year with t=0, corresponding to 1990.

Consider the given equation,

P=0.021t2+2.77t+148.9

The value of P for t=0 is,

P=0.021(0)2+2.77(0)+148.9=148.9

The value of P for t=4 is,

P=0.021(4)2+2.77(4)+148.9=159.644

The value of P for t=8 is,

P=0.021(8)2+2.77(8)+148.9=169.716

The value of P for t=12 is,

P=0.021(12)2+2.77(12)+148.9=179.116

The value of P for t=16 is,

P=0

(b)

To determine

To calculate: The value of dPdt and explain its meaning in this situation, where P (in thousands) is the population of Brazil from 1990 through 2013 modeled by the equation P=0.021t2+2.77t+148.9, where t is the year with t=0, corresponding to 1990.

(c)

To determine

To calculate: The value of dPdt for t=0,4,8,12,16,20 and 23 and also the meaning of each of these values, where P (in thousands) is the population of Brazil from 1990 through 2013 modeled by the equation P=0.021t2+2.77t+148.9, where t is the year with t=0, corresponding to 1990.

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P-12RECh-2 P-13RECh-2 P-14RECh-2 P-15RECh-2 P-16RECh-2 P-17RECh-2 P-18RECh-2 P-19RECh-2 P-20RECh-2 P-21RECh-2 P-22RECh-2 P-23RECh-2 P-24RECh-2 P-25RECh-2 P-26RECh-2 P-27RECh-2 P-28RECh-2 P-29RECh-2 P-30RECh-2 P-31RECh-2 P-32RECh-2 P-33RECh-2 P-34RECh-2 P-35RECh-2 P-36RECh-2 P-37RECh-2 P-38RECh-2 P-39RECh-2 P-40RECh-2 P-41RECh-2 P-42RECh-2 P-43RECh-2 P-44RECh-2 P-45RECh-2 P-46RECh-2 P-47RECh-2 P-48RECh-2 P-49RECh-2 P-50RECh-2 P-51RECh-2 P-52RECh-2 P-53RECh-2 P-54RECh-2 P-55RECh-2 P-56RECh-2 P-57RECh-2 P-58RECh-2 P-59RECh-2 P-60RECh-2 P-61RECh-2 P-62RECh-2 P-63RECh-2 P-64RECh-2 P-65RECh-2 P-66RECh-2 P-67RECh-2 P-68RECh-2 P-69RECh-2 P-70RECh-2 P-71RECh-2 P-72RECh-2 P-73RECh-2 P-74RECh-2 P-75RECh-2 P-76RECh-2 P-77RECh-2 P-78RECh-2 P-79RECh-2 P-80RECh-2 P-81RECh-2 P-82RECh-2 P-83RECh-2 P-84RECh-2 P-85RECh-2 P-86RECh-2 P-87RECh-2 P-88RECh-2 P-89RECh-2 P-90RECh-2 P-91RECh-2 P-92RECh-2 P-93RECh-2 P-94RECh-2 P-95RECh-2 P-96RECh-2 P-97RECh-2 P-98RECh-2 P-99RECh-2 P-100RECh-2 P-101RECh-2 P-102RECh-2 P-103RECh-2 P-104RECh-2 P-105RECh-2 P-106RECh-2 P-107RECh-2 P-108RECh-2 P-109RECh-2 P-110RECh-2 P-111RECh-2 P-112RECh-2 P-113RECh-2 P-114RECh-2 P-1TYSCh-2 P-2TYSCh-2 P-3TYSCh-2 P-4TYSCh-2 P-5TYSCh-2 P-6TYSCh-2 P-7TYSCh-2 P-8TYSCh-2 P-9TYSCh-2 P-10TYSCh-2 P-11TYSCh-2 P-12TYSCh-2 P-13TYSCh-2 P-14TYSCh-2 P-15TYSCh-2 P-16TYSCh-2 P-17TYSCh-2 P-18TYSCh-2 P-19TYSCh-2 P-20TYSCh-2 P-21TYSCh-2 P-22TYS

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