Question

If a city that currently has a population of 1000 triples in size every 8 years, what will the population be in 24 years? Is the population growth modeled by a linear function or an exponential function?

Answer 1

Present population: 1000

Population in 8 years: 1000 * 3 = 3000

Population in 16 years: 3000 * 3 = 9000

Population in 24 years: 9000 * 3 = 27,000

The population growth is modeled by an exponential function because the population grows by a higher factor than time. This is illustrated by the fact that as the number of years doubles (say from 8 years to 16 years), the population tripled from 3000 to 9000.

It is not the case in this example, but IF the population doubles as the number of years doubles, only THEN would the function be linear.

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