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A hypothetical amount 100t grows continuously at rate ln2 per year. Find its value after one year.

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

2027 JM01 考試大綱 · 2, 3 and 8. Percentage, variations, exponential growth · PDF 2 / printed page 2

TOPIC 01

Variation and financial models

Identify direct, inverse, joint and partial variation and apply stated interest or depreciation models.

Identify direct, inverse, joint and partial variation and apply stated interest or depreciation models.
Justify the method and check the conditions in a new situation.

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

01 / Transfer#Worked example

t=4

Rates are decimals; all values are idealized models with the stated period and compounding rule.

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Express the cash flow or proportional relation before calculating.

Hint 2

Use this intermediate relation.

A=Pe^{ru}

Worked solution

Express the cash flow or proportional relation before calculating.
Apply the stated relation and retain its conditions.
$A=100(4)e^{\ln2}=800$
A continuous rate is used in an exponential, not in the annual discrete-compound factor.

The requested value is 800.

Checks and common pitfalls: A continuous rate is used in an exponential, not in the annual discrete-compound factor.

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

Teacher preparation and assessment

Identify direct, inverse, joint and partial variation and apply stated interest or depreciation models.
Which condition is essential in variation and financial models?
Do a 10% increase and a 10% decrease restore the starting value?

Model or definition: Identify direct, inverse, joint and partial variation and apply stated interest or depreciation models.
$y=kx;\ y=k/x;\ y=kxz;\ y=a+kx;\ A=P(1+r)^n$
Conditions: Rates are decimals; all values are idealized models with the stated period and compounding rule.

Successive percentage changes multiply their factors rather than add their rates.