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Population growth

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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
(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.

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