Algebra 2 Flashcards: Recognize Percent Growth Or Decay

What this deck covers

This deck focuses on Recognize Percent Growth Or Decay, giving you a quick way to review the definitions, rules, and examples that matter most for Algebra 2.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Find the multiplier for “value halves every $6$ hours” per hour.

Answer: $\left(\frac{1}{2}\right)^{\frac{1}{6}}$. Per-hour multiplier is the sixth root of $\frac{1}{2}$.

Flashcard 2: Choose the model with constant percent change: $y=400\cdot(0.9)^t$ or $y=400-0.9t$.

Answer: $y=400\cdot(0.9)^t$. Exponential form with base indicates percent change.

Flashcard 3: What is the common ratio if values go $80,\ 88,\ 96.8$ at equal time steps?

Answer: $1.1$. Divide consecutive terms: $\frac{88}{80} = \frac{96.8}{88} = 1.1$.

Flashcard 4: What type of change is indicated by “increases by $5\%$ each month”?

Answer: Constant percent growth (exponential growth). Percent change per unit time indicates exponential growth.

Flashcard 5: What type of change is indicated by “decreases by $12\%$ per year”?

Answer: Constant percent decay (exponential decay). Percent change per unit time indicates exponential decay.

Flashcard 6: What is the growth factor for a constant increase of $r\%$ per interval?

Answer: $1+\frac{r}{100}$. Add the percent rate as a decimal to 1.

Flashcard 7: What is the decay factor for a constant decrease of $r\%$ per interval?

Answer: $1-\frac{r}{100}$. Subtract the percent rate as a decimal from 1.

Flashcard 8: What is the exponential form for percent growth or decay over $t$ intervals?

Answer: $A(t)=A_0\cdot b^t$. Standard exponential model with base $b$ and time $t$.

Flashcard 9: What condition on $b$ indicates exponential growth in $A(t)=A_0\cdot b^t$?

Answer: $b>1$. Base greater than 1 means the quantity increases.

Flashcard 10: What condition on $b$ indicates exponential decay in $A(t)=A_0\cdot b^t$?

Answer: $0<b<1$. Base between 0 and 1 means the quantity decreases.

Flashcard 11: What phrase signals linear (not percent) change: “adds $15$ each week” or “multiplies by $1.15$ each week”?

Answer: Adds $15$ each week (linear). Fixed amount added signals linear, not exponential change.

Flashcard 12: Which phrase signals constant percent change: “decreases by $30$ each year” or “decreases by $30\%$ each year”?

Answer: Decreases by $30\%$ each year. Percent change indicates exponential, not linear growth.

Flashcard 13: What is the percent rate per interval if the multiplier each interval is $1.08$?

Answer: $8\%$ growth per interval. Subtract 1 from the multiplier and convert to percent.

Flashcard 14: What is the percent rate per interval if the multiplier each interval is $0.93$?

Answer: $7\%$ decay per interval. Subtract the multiplier from 1 and convert to percent.

Flashcard 15: What is the multiplier for “grows by $3.5\%$ per day”?

Answer: $1.035$. Add the percent rate as a decimal to 1.

Flashcard 16: What is the multiplier for “decays by $18\%$ per hour”?

Answer: $0.82$. Subtract the percent rate as a decimal from 1.

Flashcard 17: Identify the model type for $P(t)=120\cdot(0.6)^t$.

Answer: Exponential decay. Base $0.6 < 1$ indicates exponential decay.

Flashcard 18: Identify the model type for $N(t)=50\cdot(1.2)^t$.

Answer: Exponential growth. Base $1.2 > 1$ indicates exponential growth.

Flashcard 19: What is the per-interval percent change for $A(t)=A_0\cdot(1.15)^t$?

Answer: $15\%$ growth per interval. Base $1.15$ means $15\%$ growth per interval.

Flashcard 20: What is the per-interval percent change for $A(t)=A_0\cdot(0.72)^t$?

Answer: $28\%$ decay per interval. Base $0.72$ means $28\%$ decay per interval.

Flashcard 21: Which situation is constant percent change: “$10\%$ interest yearly” or “$10$ dollars interest yearly”?

Answer: $10\%$ interest yearly. Percent interest indicates exponential compound growth.

Flashcard 22: Which situation is constant percent change: “value drops $200$ per year” or “value drops $20\%$ per year”?

Answer: Value drops $20\%$ per year. Percent change indicates exponential, not linear decay.

Flashcard 23: What is the multiplier for “increases by $25\%$ per interval”?

Answer: $1.25$. Add the percent rate as a decimal to 1.

Flashcard 24: What is the multiplier for “decreases by $25\%$ per interval”?

Answer: $0.75$. Subtract the percent rate as a decimal from 1.

Flashcard 25: Identify whether $A(t+1)=1.04\,A(t)$ represents growth or decay.

Answer: Growth. Multiplier $1.04 > 1$ indicates exponential growth.

Flashcard 26: Identify whether $A(t+1)=0.97\,A(t)$ represents growth or decay.

Answer: Decay. Multiplier $0.97 < 1$ indicates exponential decay.

Flashcard 27: What is the percent rate per interval if $A(t+1)=1.005\,A(t)$?

Answer: $0.5\%$ growth per interval. Subtract 1 from multiplier and convert to percent.

Flashcard 28: What is the percent rate per interval if $A(t+1)=0.995\,A(t)$?

Answer: $0.5\%$ decay per interval. Subtract multiplier from 1 and convert to percent.

Flashcard 29: Which description matches $b=1$ in $A(t)=A_0\cdot b^t$?

Answer: No change (constant value). Base equals 1 means no growth or decay occurs.

Flashcard 30: Which is the correct base $b$ for “decays by $9\%$ per interval” in $A(t)=A_0\cdot b^t$?

Answer: $b=0.91$. Subtract decay rate from 1: $1 - 0.09 = 0.91$.