3. The populations of two towns are modelled with the following equations, Smallville: P = 1000(1.12)
Grandville: P = 5000(1.06)
P represents the population.
t represents the time, in years since 2000.
a) Using technology, graph both equations on the same set of axes.
b) What is the initial value for each equation? How is this represented on the graph? What does each initial
value mean in the context of the problem?
c) Determine the change in population of each town from 2000 to 2001. Which town has a greater increase
over this time period? What does this imply about the steepness of the graphs in this time interval?
d) Repeat part c) for the year 2020 to 2021.
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e) Will the population of Smallville ever exceed that of Grandville? Justify your answer.