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Modeling with Functions · Paper 2 — Free Maths AA SL Practice Questions

1MasterySAQ-SReal-world applications of functions (e.g. growth models)s8 marksPaper 2~12 min
The population of a small town is growing linearly. In 2015, the population was 12 40012\,400 people. In 2023, the population was 14 20014\,200 people. Let PP represent the population tt years after 2015.
(a)
Find the linear function P(t)P(t) that models the population growth. [3 marks]
(b)
Using your model, determine the year in which the population will reach 16 00016\,000 people. [2 marks]
(c)
The town has a maximum sustainable population of 18 00018\,000 people. Determine the year in which the model predicts this limit will be reached, and evaluate one reason why the linear model may not be reliable for this prediction. [3 marks]
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