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Question

According to the population reference bureau, the world population in 2000 was 6.1 billion and increasing at an annual rate of 1.4%. Estimate the world population in 2020. Then write and evaluate an exponential function to predict the actual population, and compare it to your estimate. 

Answer 1

Joanna,

 

What follows below is exponential function you would use to predict actual population in 2020.

 

We need to express the increase in population, (1.4%) as a factor.

 

This factor is 1+r, where r is the increase in population, expressed as a decimal

1+.014 = 1.014

 

We begin with the population in 2000 and need to determine the population in 2020, 20 years later.  

Since this is exponential growth, we can think of this as each year we increase the population by 1.4%, in other words we multiply the population each year by our factor 1.014.

 

Over 20 years, this would look like

 

1.014²⁰ 

 

Population in 2020 = population in 2000 (1.014)²⁰

 

P = 6.1B (1.014)²⁰ =  8.055B

B just stands for billion.