B#. a) Given the exponential model: y = 3.470(0.70)x
(i) Does this model represent an exponential growth or decay? Justify your answer.
(ii) What is the percent rate of change?
b) Rural population decline is a serious problem in regional Australia. Some mid-sized but relatively isolated towns can lose 2% of their population per year.
(i) For an isolated town with a population of 37500, write a simplified equation that models the decline in population with respect to time. Clearly define any variables you use.
(ii) According to this model, how many will still live in the town after 12 years? Give your answer to the nearest whole number.
c) To plan for a time when it will no longer be possible to provide certain services, demographers need to know how many years it will take for the population to drop by 40%. How long will it be? Give your answer to the nearest year.
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