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Population Growth The population of the world in the year

Chapter 2, Problem 25A

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QUESTION:

Problem 25A

Population Growth The population of the world in the year 1650 was about 500 million, and in the year 2010 was 6756 million. Source: U.S. Census Bureau.

a. Assuming that the population of the world grows exponentially, find the equation for the population P(t) in millions in the year t.

b. Use your answer from part a to find the population of the world in the year 1.

c. Is your answer to part b reasonable? What does this tell you about how the population of the world grows?

Questions & Answers

QUESTION:

Problem 25A

Population Growth The population of the world in the year 1650 was about 500 million, and in the year 2010 was 6756 million. Source: U.S. Census Bureau.

a. Assuming that the population of the world grows exponentially, find the equation for the population P(t) in millions in the year t.

b. Use your answer from part a to find the population of the world in the year 1.

c. Is your answer to part b reasonable? What does this tell you about how the population of the world grows?

ANSWER:

Solution:

Step 1 of 3

In this problem, we have given that the population of the world in the year  was  million and in the year  was  million.

(a). Assuming that the population grows exponentially then the equation for the population  in million in the year  is given by

Where  and  are constant

According to question

…………….(i)

And

…………….(ii)

On dividing equation (ii) by (i), we get

.

Substitute  in equation (i)

.

Hence the required equation is .


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