LEARN · EXPLAIN · REVISE

An exponential amount grows from 4 to 32 with doubling every 2 hours. How many hours elapsed?

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 / Transfer#Your turn

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

First remove the initial amount.

Worked solution

Translate the context into an exponential or logarithmic equation and check what the model assumes.
Calculate or simplify this relation.
$42^{t/2}=32\Rightarrow2^{t/2}=8\Rightarrow t=6$
Three doublings require six hours.

The requested value is 6.

Checks and common pitfalls: Three doublings require six hours.

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.