Problem preview

F-BF.1.a Warmup M2-014-A12-V03

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

Write an explicit function model from a context and choose a reasonable domain

Problem

From the timeline, model a population starting at \(300\) and growing \(5\%~\text{at}~\text{each}~\text{year}\text{-}\text{end}\) for \(10~\text{years}\). Define \(t\) as completed years, derive the multiplier and explicit function, and state the finite discrete domain including both endpoints.

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P(t) = 300(1.05)t. The input meaning and recorded-year domain are not given.

P(t) = 300(1.05)t, where t is completed years. Because values are recorded yearly for 10 years, the discrete domain is 0, 1, ..., 10.

P(t) = 300(1.05)t for every real t from 0 to 10. The stated records occur yearly, so the intended domain is discrete.

P(t) = 300(1.05)t for negative and post-study years. Those inputs are outside the 10-year recording context.

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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: Write an explicit function model from a context and choose a reasonable domain