World Population Growth

Question

In 2010, the world population was 6.9 billion, and the exponential growth rate was 1.1% per year.

a) Find the exponential growth function,

b) Predict the world population in 2014, 

c) when will the world population be 8.0 billion

Answer 1

A growth equation takes the form:

 

P(t) = a(r)^t,

 

where a = initial population (in our case, in billions), r = rate of growth in decimal form, t = years after initial year, and P(t) is population after t years. For an initial year of 2010, you've been given a = 6.9 and r = 1.011 (the population after another year passes is 101.1% of its previous value). Plug those in to get the exponential growth function:

 

P(t) = 6.9(1.011)^t

 

 

 

The world population in 2014 can be predicted by plugging in t = 4, since 2014 is 4 years after 2010:

 

P(t) = 6.9(1.011)⁴

P(t) = 6.9(1.0447)

P(t) = 7.209

 

The world population will be approximately 7.2 billion in 2014.

 

 

 

To find when the world population will be 8.0 billion, plug in P(t) = 8 and solve for t:

 

8 = 6.9(1.011)^t

1.159 = 1.011^t

log_1.011(1.159) = t

13.488 = t

 

The world population will reach 8.0 billion after approximately 13.5 years. With an initial year of 2010, this falls halfway through 2023.