The population(in millions) of a country in 2015 is P = 44.4 million,
the expected continuous annual rate of change k = - 0.006 and
t = 5 corresponds to the year 2015.
(a) The Exponential growth model
(b) To predict the population of the country in 2030 using the given model.
(c) The relationship between the sign of k and the change in population for the country.
(a) To find the Exponential growth model for the population by letting t = 5 correspond to 2015. The formula used to find the Exponential growth mode is
putting values of p, k & t in the above equation
Therefore,the exponential growth model is
(b)Using the above Exponential growth model to predict the population of the country in 2030.
The year 2030 corresponds to t = 20.
Then the population will be,
(c) The relationship between the sign of k and the change in population for the country:
Here, the sign of k is negative (k < 0). With a positive relationship, these limiting factors increase with the size of the population and limit growth as population size increases. With a negative relationship, population growth is decreases and becomes less limited as it grows.
As we have, k < 0, the population is declining.