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
