Problema Solution
The population of a rural city follows the wxpoential growth model P(t)=1900e^0.036t where t is the number of years after 1986.
a) What was the population of this city in 1986?
b) What is the relative growth rate as a percent?
c) Use this model to approximate the population in 2037.
Answer provided by our tutors
given , P(t) = 1900e0.036t
comparing with standard equation of growth model P(t) = Aext
where t is the time interval
and x is the relative rate of increase in population
we get ,
A=1900
x=0.036 = (0.036x100)% = 3.6 %
as given t is the time after 1986 , then taking 1986 as the reference
a) in 1986 , t = 0
therefore, P(0) = 1900e0.036(0)= 1900e0 = 1900(1) = 1900 = initial population of city
b) relative growth rate = x = 3.6 %
c) for population in 2037
t = 2037 - 1986 =51
therefore,
P(51) = 1900e0.036(51)= 1900(6.27) = 11915.6 = population in 2037