Problem preview

F-BF.1.a Warmup M2-014-A11-V02

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Choose whether a context is modeled by a quadratic or an exponential function

Problem

Classify a population model that increases \(8\%\) each year. Convert the percent change to multiplier \(1.08\), write a generic model from initial population \(P_{0}\), and explain why repeated multiplication determines the function type.

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It is best modeled by a quadratic function because the population goes up every year, so the growth keeps getting larger over time.

It is best modeled by a quadratic function because 8% each year means adding the same amount each year to the population.

It is best modeled by an exponential function because increasing by 8% each year means multiplying by the same factor, 1.08, each year.

It is best modeled by an exponential function because any situation involving a percent must be exponential, even without thinking about how it changes each year.

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Curriculum context

Course: Math II
Standard: F-BF.1.a
Category: Functions
Domain: Building Functions
Objective: Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type: Choose whether a context is modeled by a quadratic or an exponential function