The function P(t)=(1436.53)⋅(1.01395)^t is used to model the world's population(in millions) where t is the number of years after 1900.?

聰明羊

2015-11-14 8:16 am

a. According to this model, what was the population in 2000? What is the population in 2015? Show your calculations.
b. According to this model, what was the rate of increase in the world population in 2000? What is it in 2015? Show your calculations and give the correct units.

回答 (1)

Lopez

2015-11-15 7:33 am

✔ 最佳答案

a.
P( 2000 - 1900 )
= P(100)
= 1436.53 * 1.01395^100
≒ 5741

P( 2015 - 1900 )
= P(115)
= 1436.53 * 1.01395^115
≒ 7067

b.
P(t) = 1436.53 * 1.01395^t

P ' (t)
= 1436.53 * 1.01395^t * ln 1.01395
= ( 1436.53 * ln 1.01395 ) * 1.01395^t

P ' ( 2000 - 1900 )
= P ' ( 100 )
= ( 1436.53 * ln 1.01395 ) * 1.01395^100
≒ 80

P ' ( 2015 - 1900 )
= P ' ( 115 )
= ( 1436.53 * ln 1.01395 ) * 1.01395^115
≒ 98

Ans:
a.
5741 millions in 2000
7067 millions in 2015
b.
80 millions / year in 2000
98 millions / year in 2015

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