Question

The population of Guatemala in 2000 was 12.7 million.

1. Assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2020? Answer (in millions): P(t)=

2. Assuming exponential growth, what would be the size of the population after time t (measured in years after 2000) if the population was 30 million in 2125?
Answer (in millions): P(t)=

Answer 1

Since the population of Guatemala follows an exponential growth, therefore the equation describing the population over time should be in the form:

p = p0 (1 + r)^t

where,

p = is the population at specified time t

p0 = is the initial population (measured starting year 2000) = 12.7 m

r = the growth rate

t = time in years

 

A. Calculating for the growth rate r when p = 30 and t = 20:

30 = 12.7 (1 + r)^20

1 + r = (30 / 12.7)^(1/20)

r = (30 / 12.7)^(1/20) – 1

r = 0.0440

 

So the equation is:

p = p0 (1.0440)^t

 

 

B. Calculating for the growth rate r when p = 30 and t = 125:

30 = 12.7 (1 + r)^125

1 + r = (30 / 12.7)^(1/125)

r = (30 / 12.7)^(1/125) – 1

r = 0.0069

 

So the equation is:

p = p0 (1.0069)^t