Population growth
posted by Sinha .
The population P of a particular city, Metropia, is growing at a rate proportional to the
current population.
The population at time t years is modelled by the equation P = Aekt where A and k are
constants.
(a) With the aid of appropriate examples, explain how the growth of P over time
would be influenced by:
(i) The magnitude of A
(ii) The magnitude of k
(iii) The sign of k
(b) If the population of Metropia was 1,000,000 in 2005 (at t = 0) and 1,072,500
in 2007, determine the values of A and k and hence write an equation to model
Metropia’s population with respect to time.
(c) Predict the population of Metropia in the year 2012.
(d) Determine the expected length of time it would take for the population of Metropia
to double.

What is your question about this?
Respond to this Question
Similar Questions

math
the population of a southern city follows the exponential law. If the population doubled in size over an 18 month period and the current population in 10000, what will be the population 2 years from now? 
CACULUS EXPONENTIAL GROWTH
A population of animals in an ecological niche is growing in time so that it's rate of growth dp/dt is related to its current size by the differential equation dp/dt = 900/p^2. If time is measured in years and initially there are P(0) … 
POPULATION
If a population consists of 10,000 individuals at time t=0 years (P0), and the annual growth rate (excess of births over deaths) is 3% (GR), what will the population be after 1, 15 and 100 years (n)? 
Algebra
Solve. The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke^0.12t where k is a constant and t is the time in years. If the current population is 15,000, in how … 
Maths B question  population
The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P = Aekt where A and k are constants. (a) With the aid of appropriate … 
Maths B  Population Growth
The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P=¡¼Ae¡½^kt where A and k are constants. With the aid of appropriate … 
Maths
The population P of a particular city, Metropia, is growing at a rate proportional to the current population. The population at time t years is modelled by the equation P=Ae^kt where A and k are constants. With the aid of appropriate … 
Calculus
The CIA published data about foreign countries on its web page. In particular they show total population as well as population growth. If a student is looking at Russia, they will see that the total population of Russia is declining. … 
Calculus
The rate of growth of a particular population is given by dP/dt=50t^2100t^3/2 where P is the population size and t is the time in years. The initial population is 25,000. Find the population function. Estimate how many years it will … 
calculus
The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.3. The initial population is 40. (1) What is the population after 30 …