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: Which statement indicates constant percent growth relative to the current amount?

Answer: "Increases by the same percent each interval". Same percent each interval indicates exponential growth.

Flashcard 2: What is the percent rate per interval if the common ratio in a table is $\frac{4}{5}$?

Answer: $20\%$ decay per interval. Convert fraction to percent: $1 - \frac{4}{5} = 0.20 = 20\%$.

Flashcard 3: 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 4: What is the percent growth rate per year if a quantity "doubles every year"?

Answer: $100\%$ growth per year. Doubling means $100\%$ increase from original amount.

Flashcard 5: What is the common ratio if values go $200, 150, 112.5$ at equal time steps?

Answer: $0.75$. Divide consecutive terms: $\frac{150}{200} = \frac{112.5}{150} = 0.75$.

Flashcard 6: 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 7: Identify the common ratio if a quantity grows by $30\%$ per interval.

Answer: $1.3$. Add growth rate to 1: $1 + 0.30 = 1.3$.

Flashcard 8: Identify the base $b$ if "decays by $2\%$ each interval" is modeled by $A(t)=A_0\cdot b^t$.

Answer: $b=0.98$. Subtract decay rate from 1: $1 - 0.02 = 0.98$.

Flashcard 9: 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 10: What is the multiplier for "grows by $3.5\%$ per day"?

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

Flashcard 11: Identify the model type for $P(t)=120\cdot(0.6)^t$.

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

Flashcard 12: Which phrase signals exponential decay: "retains $85\%$ each year" or "loses $85$ units each year"?

Answer: Retains $85\%$ each year. Percentage retained indicates exponential decay model.

Flashcard 13: Identify whether $A(t+1)=1.04\,A(t)$ represents growth or decay.

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

Flashcard 14: What is the multiplier for "increases by $25\%$ per interval"?

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

Flashcard 15: 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 16: 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 17: What is the multiplier if a quantity "retains $85\%$ each year"?

Answer: $0.85$. Retaining $85\%$ means multiplier is $0.85$.

Flashcard 18: 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 19: What is the percent rate per step if values go $200,\ 150,\ 112.5$ at equal time steps?

Answer: $25\%$ decay per step. Common ratio $0.75$ means $25\%$ decay per step.

Flashcard 20: 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 21: 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 22: 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 23: Identify the base $b$ if "grows by $2\%$ each interval" is modeled by $A(t)=A_0\cdot b^t$.

Answer: $b=1.02$. Add growth rate to 1: $1 + 0.02 = 1.02$.

Flashcard 24: 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 25: 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 26: Identify the key recognition clue for constant additive change in a table of values.

Answer: A constant difference between successive outputs. Constant difference indicates linear (additive) change.

Flashcard 27: Which statement indicates NOT constant percent change: "increases by $5$ each day" or "increases by $5\%$ each day"?

Answer: Increases by $5$ each day. Fixed amount added indicates linear, not percent change.

Flashcard 28: Which is the correct base $b$ for "grows by $9\%$ per interval" in $A(t)=A_0\cdot b^t$?

Answer: $b=1.09$. Add growth rate to 1: $1 + 0.09 = 1.09$.

Flashcard 29: 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 30: Identify whether $A(t+1)=0.97\,A(t)$ represents growth or decay.

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

Flashcard 31: 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: $1 - 0.09 = 0.91$.

Flashcard 32: What is the multiplier if a quantity "is $120\%$ of the previous value each interval"?

Answer: $1.2$. Being $120\%$ of previous means multiplier is $1.2$.

Flashcard 33: 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 34: Which option indicates constant percent decay: $A(t)=A_0\cdot(0.85)^t$ or $A(t)=A_0-0.85t$?

Answer: $A(t)=A_0\cdot(0.85)^t$. Base $0.85 < 1$ in exponential form indicates decay.

Flashcard 35: What is the multiplier for "decays by $18\%$ per hour"?

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

Flashcard 36: What is the multiplier for "decreases by $25\%$ per interval"?

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

Flashcard 37: Which option indicates exponential change: $A(t)=A_0+5t$ or $A(t)=A_0\cdot(1.05)^t$?

Answer: $A(t)=A_0\cdot(1.05)^t$. Base raised to power $t$ indicates exponential change.

Flashcard 38: 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 39: What is the percent rate per interval if the common ratio in a table is $\frac{5}{4}$?

Answer: $25\%$ growth per interval. Convert fraction to percent: $\frac{5}{4} - 1 = 0.25 = 25\%$.

Flashcard 40: 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 41: 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 42: What is the percent rate per step if values go $80,\ 88,\ 96.8$ at equal time steps?

Answer: $10\%$ growth per step. Common ratio $1.1$ means $10\%$ growth per step.

Flashcard 43: 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 44: Which is constant percent change: ratios $\frac{A(t+1)}{A(t)}$ constant or differences $A(t+1)-A(t)$ constant?

Answer: Ratios $\frac{A(t+1)}{A(t)}$ constant. Constant ratio between consecutive terms indicates percent change.

Flashcard 45: Identify the model type for $N(t)=50\cdot(1.2)^t$.

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

Flashcard 46: What is the common ratio if values go $200,\ 150,\ 112.5$ at equal time steps?

Answer: $0.75$. Divide consecutive terms: $\frac{150}{200} = \frac{112.5}{150} = 0.75$.

Flashcard 47: Identify whether "doubles every year" represents constant percent growth per year.

Answer: Yes; multiplier $2$ per year. Doubling means multiplying by $2$ each year.

Flashcard 48: Find the multiplier for "value is multiplied by $3$ every $2$ days" per day.

Answer: $\sqrt{3}$. Per-day multiplier is the square root of $3$.

Flashcard 49: Identify the key recognition clue for constant percent change in a table of values.

Answer: A constant ratio between successive outputs. Constant ratio indicates exponential (percent) change.

Flashcard 50: 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 51: 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 52: 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 53: Identify the common ratio if a quantity decays by $30\%$ per interval.

Answer: $0.7$. Subtract decay rate from 1: $1 - 0.30 = 0.7$.

Flashcard 54: Which situation is constant percent change: "$10\%$ interest yearly" or "$10$ dollars interest yearly"?

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