Card 1 of 20
EasyStudy card 1
Prompt
What model represents per-period growth at decimal rate \(r\)?
Answer
\(A=P(1+r)^t\).
MathChapter 12: Composition, Recursion, and Exponential Functions
Flashcards
Exponential Growth and Decay Flashcards
Twenty recall-focused cards on percent multipliers, compound growth, decay, doubling, half-life, fractional intervals, and model validation.
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Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What model represents per-period decay at decimal rate \(r\)?
Answer
\(A=P(1-r)^t\).
Card 3 of 20
EasyStudy card 3
Prompt
What multiplier represents a \(6\%\) increase?
Answer
\(1.06\).
Card 4 of 20
EasyStudy card 4
Prompt
What multiplier represents a \(12\%\) decrease?
Answer
\(0.88\).
Card 5 of 20
EasyStudy card 5
Prompt
How is \(4.5\%\) written as a decimal rate?
Answer
\(0.045\).
Card 6 of 20
EasyStudy card 6
Prompt
What does \(P\) represent in these models?
Answer
The initial amount, which the model returns at \(t=0\).
Card 7 of 20
EasyStudy card 7
Prompt
What does \(t\) represent in \(P(1\pm r)^t\)?
Answer
The number of periods matching the stated rate.
Card 8 of 20
MediumStudy card 8
Prompt
What is the doubling-time model?
Answer
\(A=P\cdot2^{t/d}\).
Card 9 of 20
MediumStudy card 9
Prompt
What does \(t/d\) count in a doubling model?
Answer
The number of doubling intervals elapsed.
Card 10 of 20
MediumStudy card 10
Prompt
What is the half-life model?
Answer
\(A=P(\frac12)^{t/d}\).
Card 11 of 20
MediumStudy card 11
Prompt
What does one half-life do to the current amount?
Answer
It multiplies the amount then remaining by \(\frac12\).
Card 12 of 20
MediumStudy card 12
Prompt
After three doubling intervals, what multiple of \(P\) remains?
Answer
\(8P\).
Card 13 of 20
MediumStudy card 13
Prompt
After four half-lives, what fraction of \(P\) remains?
Answer
\(\frac{P}{16}\).
Card 14 of 20
MediumStudy card 14
Prompt
Must \(t/d\) be a whole number?
Answer
No. Fractional numbers of doubling or half-life intervals are valid.
Card 15 of 20
MediumStudy card 15
Prompt
Why is \(P(0.06)^t\) wrong for \(6\%\) growth?
Answer
It uses only the added fraction; growth must retain the original amount with factor \(1.06\).
Card 16 of 20
MediumStudy card 16
Prompt
How should two model values be compared accurately?
Answer
Evaluate both with full precision at the requested time, subtract, then round once.
Card 17 of 20
HardStudy card 17
Prompt
A quantity doubles every \(5\) years. What exponent is used after \(12\) years?
Answer
\(12/5=2.4\).
Card 18 of 20
HardStudy card 18
Prompt
A sample has half-life \(8\) days. What exponent is used after \(20\) days?
Answer
\(20/8=2.5\).
Card 19 of 20
HardStudy card 19
Prompt
What two substitutions quickly validate a doubling model?
Answer
Check \(A(0)=P\) and \(A(d)=2P\).
Card 20 of 20
HardStudy card 20
Prompt
What two substitutions quickly validate a half-life model?
Answer
Check \(A(0)=P\) and \(A(d)=P/2\).
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