LEARN · EXPLAIN · REVISE

A population is 200 and increases by 10% each year. Find it after two years.

Read the idea, work independently, then explain what changed.

高一必修第一册(A版).pdf · 4.5 · PDF 149 / printed page 142

TOPIC 01

Applications of functions II

Build understanding of applications of functions ii through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Worked example

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the context into an exponential or logarithmic equation and check what the model assumes.

Hint 2

The second percentage applies to the enlarged population.

Worked solution

Translate the context into an exponential or logarithmic equation and check what the model assumes.
Calculate or simplify this relation.
$200(1.1)^2=242$
This is compounding, not a single 20% increase.

The requested value is 242.

Checks and common pitfalls: This is compounding, not a single 20% increase.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Interpret and use applications of functions ii with domain checks.
Multiplicative change: Constant ratios lead to exponential models; logarithms solve elapsed-time questions.
Zeros and evidence: Continuity plus a sign change gives a zero; model validity still needs evidence.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Constant ratios lead to exponential models; logarithms solve elapsed-time questions.
Expected reasoning: Continuity plus a sign change gives a zero; model validity still needs evidence.
Expected correction: A fitted trend does not justify unlimited extrapolation.