Algebra 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.

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 percent rate per interval for $A(t)=90(1.07)^t$.

Answer: $7\%$ increase. Base $1.07 = 1 + 0.07$, so the rate is $7\%$ increase.

Flashcard 2: What decimal is equivalent to a $12\%$ growth rate?

Answer: $r=0.12$. Convert $12\%$ to decimal: $12 ÷ 100 = 0.12$.

Flashcard 3: Find the percent rate per interval for $A(t)=90(0.93)^t$.

Answer: $7\%$ decrease. Base $0.93 = 1 - 0.07$, so the rate is $7\%$ decrease.

Flashcard 4: What is the value of $b$ in $A(t)=A_0b^t$ if the quantity decreases by $18\%$ each interval?

Answer: $b=0.82$. Decrease by $18\%$ means $b = 1 - 0.18 = 0.82$.

Flashcard 5: What feature distinguishes linear change from exponential change in a table?

Answer: Constant difference (not constant ratio). Each y-value minus the previous equals the same number (constant difference).

Flashcard 6: Which description matches $A(t)=A_0b^t$ when $b>1$?

Answer: Exponential growth. When $b > 1$, each multiplication makes the quantity larger.

Flashcard 7: What is the growth factor for $3\%$ growth per interval?

Answer: $1.03$. Growth factor is $1 + 0.03 = 1.03$.

Flashcard 8: Identify the model type: "A population doubles every $5$ years."

Answer: Exponential growth. Doubling represents multiplication by 2 each interval, which is exponential growth.

Flashcard 9: What is the growth factor for $3\%$ growth per interval?

Answer: $1.03$. Growth factor is $1 + 0.03 = 1.03$.

Flashcard 10: What is the common ratio for values $50,60,72$ at equal intervals?

Answer: $1.2$. Each consecutive ratio: $\frac{60}{50} = 1.2$ and $\frac{72}{60} = 1.2$.

Flashcard 11: What model matches "starts at $64$ and halves each interval"?

Answer: $A(t)=64(0.5)^t$. Initial value $64$, halving means multiplier is $0.5$.

Flashcard 12: Identify the model type: "A car loses $20\%$ of its value each year."

Answer: Exponential decay. Losing a constant percentage each period creates exponential decay.

Flashcard 13: What is the multiplier for "increases by $30\%$ each interval"?

Answer: $1.30$. For $30\%$ increase: $1 + 0.30 = 1.30$.

Flashcard 14: What is the growth factor (multiplier) for $8\%$ growth per interval?

Answer: $1.08$. Growth factor is $1 + 0.08 = 1.08$.

Flashcard 15: What feature distinguishes exponential change from linear change in a table?

Answer: Constant ratio (not constant difference). Each y-value divided by the previous equals the same number (constant ratio).

Flashcard 16: What is the percent rate for a common ratio of $1.2$ per interval?

Answer: $20\%$ increase. Ratio $1.2 = 1 + 0.2$, so the increase is $20\%$.

Flashcard 17: Identify the type: "The amount is multiplied by $1.15$ each week."

Answer: Exponential growth. Multiplier $1.15 > 1$ indicates the quantity increases each period.

Flashcard 18: Identify whether the change is constant percent: values $100,110,121$ at equal intervals.

Answer: Yes; ratio is constant at $1.1$. Ratios: $\frac{110}{100} = 1.1$ and $\frac{121}{110} = 1.1$ are constant.

Flashcard 19: What is the growth factor (multiplier) for $8\%$ growth per interval?

Answer: $1.08$. Growth factor is $1 + 0.08 = 1.08$.

Flashcard 20: What model matches "starts at $500$ and increases by $6\%$ each year"?

Answer: $A(t)=500(1.06)^t$. Initial value $500$, growth factor $1 + 0.06 = 1.06$, time variable $t$.

Flashcard 21: What key phrase signals constant percent growth or decay each time interval?

Answer: "Increases/decreases by $r\%$ each (time) interval". This phrase directly indicates a constant percentage change each time period.

Flashcard 22: What model matches "starts at $1200$ and doubles every interval"?

Answer: $A(t)=1200(2)^t$. Initial value $1200$, doubling means multiplier is $2$.

Flashcard 23: What model matches "starts at $500$ and increases by $6\%$ each year"?

Answer: $A(t)=500(1.06)^t$. Initial value $500$, growth factor $1 + 0.06 = 1.06$, time variable $t$.

Flashcard 24: What feature distinguishes linear change from exponential change in a table?

Answer: Constant difference (not constant ratio). Each y-value minus the previous equals the same number (constant difference).

Flashcard 25: What key phrase signals constant percent growth or decay each time interval?

Answer: "Increases/decreases by $r\%$ each (time) interval". This phrase directly indicates a constant percentage change each time period.

Flashcard 26: What is the per-interval multiplier for "increases by $r\%$" written with $r$ as a percent?

Answer: $1+\frac{r}{100}$. When $r$ is a percent value, divide by $100$ then add to $1$.

Flashcard 27: Identify the type: "The amount is multiplied by $1.15$ each week."

Answer: Exponential growth. Multiplier $1.15 > 1$ indicates the quantity increases each period.

Flashcard 28: What percent change corresponds to a multiplier of $1.25$ per interval?

Answer: $25\%$ increase. Multiplier $1.25 = 1 + 0.25$, so the increase is $25\%$.

Flashcard 29: Identify the model type: "A population doubles every $5$ years."

Answer: Exponential growth. Doubling represents multiplication by 2 each interval, which is exponential growth.

Flashcard 30: What is the multiplier for "triples each interval"?

Answer: $3$. Tripling means multiplying by 3 each interval.

Flashcard 31: Identify whether the change is constant percent: values $100,110,121$ at equal intervals.

Answer: Yes; ratio is constant at $1.1$. Ratios: $\frac{110}{100} = 1.1$ and $\frac{121}{110} = 1.1$ are constant.

Flashcard 32: Which equation has a constant percent rate: $y=300(0.8)^t$ or $y=300-0.8t$?

Answer: $y=300(0.8)^t$. The exponential form has a constant base raised to variable power.

Flashcard 33: What is the general exponential form for constant percent change over $t$ intervals?

Answer: $A(t)=A_0(1+r)^t$. Standard exponential function where $A_0$ is initial value and $(1+r)$ is the growth factor.

Flashcard 34: What is the common ratio for values $50,60,72$ at equal intervals?

Answer: $1.2$. Each consecutive ratio: $\frac{60}{50} = 1.2$ and $\frac{72}{60} = 1.2$.

Flashcard 35: What is the value of $b$ in $A(t)=A_0b^t$ if the quantity decreases by $18\%$ each interval?

Answer: $b=0.82$. Decrease by $18\%$ means $b = 1 - 0.18 = 0.82$.

Flashcard 36: Which description matches $A(t)=A_0b^t$ when $0<b<1$?

Answer: Exponential decay. When $0 < b < 1$, each multiplication makes the quantity smaller.

Flashcard 37: Which situation uses constant percent change: "earns $5\%$ interest yearly" or "earns $50$ yearly"?

Answer: "Earns $5\%$ interest yearly". Percentage interest creates exponential growth, not constant addition.

Flashcard 38: What is the decay factor for $3\%$ decay per interval?

Answer: $0.97$. Decay factor is $1 - 0.03 = 0.97$.

Flashcard 39: Which option represents exponential growth: $A(t)=50+3t$ or $A(t)=50(1.03)^t$?

Answer: $A(t)=50(1.03)^t$. The exponential form with base $1.03 > 1$ indicates growth, not linear increase.

Flashcard 40: What is the per-interval multiplier for "decreases by $r\%$" written with $r$ as a percent?

Answer: $1-\frac{r}{100}$. When $r$ is a percent value, divide by $100$ then subtract from $1$.

Flashcard 41: Identify whether the change is constant percent: values $100,120,140$ at equal intervals.

Answer: No; differences are constant, not ratios. Differences of $20$ are constant, indicating linear (not exponential) change.

Flashcard 42: Which situation uses constant percent change: "earns $5\%$ interest yearly" or "earns $50$ yearly"?

Answer: "Earns $5\%$ interest yearly". Percentage interest creates exponential growth, not constant addition.

Flashcard 43: What is the multiplier for a $r\%$ increase per interval?

Answer: $1+r$ (with $r$ as a decimal). Add the decimal rate to 1 to get the growth multiplier.

Flashcard 44: What percent change corresponds to a multiplier of $0.6$ per interval?

Answer: $40\%$ decrease. Multiplier $0.6 = 1 - 0.4$, so the decrease is $40\%$.

Flashcard 45: Identify the unit interval in "grows by $5\%$ per month."

Answer: Month. The phrase 'per month' identifies month as the time interval unit.

Flashcard 46: Which equation has a constant percent rate: $y=300(0.8)^t$ or $y=300-0.8t$?

Answer: $y=300(0.8)^t$. The exponential form has a constant base raised to variable power.

Flashcard 47: What is the percent rate for a common ratio of $1.2$ per interval?

Answer: $20\%$ increase. Ratio $1.2 = 1 + 0.2$, so the increase is $20\%$.

Flashcard 48: What model matches "starts at $80$ and decreases by $12\%$ each hour"?

Answer: $A(t)=80(0.88)^t$. Initial value $80$, decay factor $1 - 0.12 = 0.88$, time variable $t$.

Flashcard 49: What is the multiplier for a $r\%$ decrease per interval?

Answer: $1-r$ (with $r$ as a decimal). Subtract the decimal rate from 1 to get the decay multiplier.

Flashcard 50: Identify the type: "The amount is multiplied by $0.92$ each day."

Answer: Exponential decay. Multiplier $0.92 < 1$ indicates the quantity decreases each period.

Flashcard 51: What is the multiplier for "increases by $30\%$ each interval"?

Answer: $1.30$. For $30\%$ increase: $1 + 0.30 = 1.30$.

Flashcard 52: What is the decay factor (multiplier) for $15\%$ decay per interval?

Answer: $0.85$. Decay factor is $1 - 0.15 = 0.85$.

Flashcard 53: What is the multiplier for "decreases by $30\%$ each interval"?

Answer: $0.70$. For $30\%$ decrease: $1 - 0.30 = 0.70$.

Flashcard 54: What percent change corresponds to a multiplier of $0.6$ per interval?

Answer: $40\%$ decrease. Multiplier $0.6 = 1 - 0.4$, so the decrease is $40\%$.

Flashcard 55: What is the multiplier for "halves each interval"?

Answer: $0.5$. Halving means multiplying by $\frac{1}{2} = 0.5$ each interval.

Flashcard 56: What is the starting value $A_0$ in the model $A(t)=A_0(1+r)^t$?

Answer: The value when $t=0$. $A_0$ represents the initial amount before any time has passed.

Flashcard 57: What decimal is equivalent to a $7\%$ decay rate?

Answer: $r=0.07$. Convert $7\%$ to decimal: $7 ÷ 100 = 0.07$.

Flashcard 58: Identify the constant percent rate for values $30,33,36.3$ at equal intervals.

Answer: $10\%$ increase (ratio $1.1$). Consecutive ratios: $\frac{33}{30} = 1.1$ and $\frac{36.3}{33} = 1.1$.

Flashcard 59: What is the multiplier for "halves each interval"?

Answer: $0.5$. Halving means multiplying by $\frac{1}{2} = 0.5$ each interval.

Flashcard 60: Which option shows constant percent change: differences $+5,+5,+5$ or ratios $\times 1.05,\times 1.05$?

Answer: Ratios $\times 1.05$ (constant ratio). Constant ratios indicate exponential change; constant differences indicate linear.

Flashcard 61: Identify the type: "The amount is multiplied by $0.92$ each day."

Answer: Exponential decay. Multiplier $0.92 < 1$ indicates the quantity decreases each period.

Flashcard 62: Identify the unit interval in "grows by $5\%$ per month."

Answer: Month. The phrase 'per month' identifies month as the time interval unit.

Flashcard 63: Identify the unit interval in "decays by $2\%$ per year."

Answer: Year. The phrase 'per year' identifies year as the time interval unit.

Flashcard 64: What is the decay factor (multiplier) for $15\%$ decay per interval?

Answer: $0.85$. Decay factor is $1 - 0.15 = 0.85$.

Flashcard 65: Which option represents exponential decay: $P(t)=200(0.9)^t$ or $P(t)=200-0.9t$?

Answer: $P(t)=200(0.9)^t$. The exponential form with base $0.9 < 1$ indicates decay, not linear decrease.

Flashcard 66: Identify the unit interval in "decays by $2\%$ per year."

Answer: Year. The phrase 'per year' identifies year as the time interval unit.

Flashcard 67: Which phrase indicates exponential decay rather than growth: "grows by" or "decreases by"?

Answer: "Decreases by" (a constant percent each interval). 'Decreases by' indicates the quantity is getting smaller over time.

Flashcard 68: What is the starting value $A_0$ in the model $A(t)=A_0(1+r)^t$?

Answer: The value when $t=0$. $A_0$ represents the initial amount before any time has passed.

Flashcard 69: What percent change corresponds to a multiplier of $0.98$ per interval?

Answer: $2\%$ decrease. Multiplier $0.98 = 1 - 0.02$, so the decrease is $2\%$.

Flashcard 70: What is the decay factor for $3\%$ decay per interval?

Answer: $0.97$. Decay factor is $1 - 0.03 = 0.97$.

Flashcard 71: What percent change corresponds to a multiplier of $0.98$ per interval?

Answer: $2\%$ decrease. Multiplier $0.98 = 1 - 0.02$, so the decrease is $2\%$.

Flashcard 72: What feature distinguishes exponential change from linear change in a table?

Answer: Constant ratio (not constant difference). Each y-value divided by the previous equals the same number (constant ratio).

Flashcard 73: Which option represents exponential decay: $P(t)=200(0.9)^t$ or $P(t)=200-0.9t$?

Answer: $P(t)=200(0.9)^t$. The exponential form with base $0.9 < 1$ indicates decay, not linear decrease.

Flashcard 74: Which phrase indicates exponential decay rather than growth: "grows by" or "decreases by"?

Answer: "Decreases by" (a constant percent each interval). 'Decreases by' indicates the quantity is getting smaller over time.

Flashcard 75: Find the percent rate per interval for $A(t)=90(1.07)^t$.

Answer: $7\%$ increase. Base $1.07 = 1 + 0.07$, so the rate is $7\%$ increase.

Flashcard 76: What is the percent rate for a common ratio of $0.75$ per interval?

Answer: $25\%$ decrease. Ratio $0.75 = 1 - 0.25$, so the decrease is $25\%$.

Flashcard 77: Find the percent rate per interval for $A(t)=90(0.93)^t$.

Answer: $7\%$ decrease. Base $0.93 = 1 - 0.07$, so the rate is $7\%$ decrease.

Flashcard 78: Identify the constant percent rate for values $200,160,128$ at equal intervals.

Answer: $20\%$ decrease (ratio $0.8$). Consecutive ratios: $\frac{160}{200} = 0.8$ and $\frac{128}{160} = 0.8$.

Flashcard 79: Identify the constant percent rate for values $30,33,36.3$ at equal intervals.

Answer: $10\%$ increase (ratio $1.1$). Consecutive ratios: $\frac{33}{30} = 1.1$ and $\frac{36.3}{33} = 1.1$.

Flashcard 80: What is the multiplier for "triples each interval"?

Answer: $3$. Tripling means multiplying by 3 each interval.

Flashcard 81: What model matches "starts at $64$ and halves each interval"?

Answer: $A(t)=64(0.5)^t$. Initial value $64$, halving means multiplier is $0.5$.

Flashcard 82: Which option represents exponential growth: $A(t)=50+3t$ or $A(t)=50(1.03)^t$?

Answer: $A(t)=50(1.03)^t$. The exponential form with base $1.03 > 1$ indicates growth, not linear increase.

Flashcard 83: What model matches "starts at $80$ and decreases by $12\%$ each hour"?

Answer: $A(t)=80(0.88)^t$. Initial value $80$, decay factor $1 - 0.12 = 0.88$, time variable $t$.

Flashcard 84: What percent change corresponds to a multiplier of $1.04$ per interval?

Answer: $4\%$ increase. Multiplier $1.04 = 1 + 0.04$, so the increase is $4\%$.

Flashcard 85: Identify whether the change is constant percent: values $100,120,140$ at equal intervals.

Answer: No; differences are constant, not ratios. Differences of $20$ are constant, indicating linear (not exponential) change.

Flashcard 86: Which description matches $A(t)=A_0b^t$ when $b>1$?

Answer: Exponential growth. When $b > 1$, each multiplication makes the quantity larger.

Flashcard 87: Identify the model type: "A car loses $20\%$ of its value each year."

Answer: Exponential decay. Losing a constant percentage each period creates exponential decay.

Flashcard 88: Which option shows constant percent change: differences $+5,+5,+5$ or ratios $\times 1.05,\times 1.05$?

Answer: Ratios $\times 1.05$ (constant ratio). Constant ratios indicate exponential change; constant differences indicate linear.

Flashcard 89: What percent change corresponds to a multiplier of $1.25$ per interval?

Answer: $25\%$ increase. Multiplier $1.25 = 1 + 0.25$, so the increase is $25\%$.

Flashcard 90: What is the multiplier for "decreases by $30\%$ each interval"?

Answer: $0.70$. For $30\%$ decrease: $1 - 0.30 = 0.70$.

Flashcard 91: What model matches "starts at $1200$ and doubles every interval"?

Answer: $A(t)=1200(2)^t$. Initial value $1200$, doubling means multiplier is $2$.

Flashcard 92: Identify the model type: "A tank drains $3$ gallons per minute."

Answer: Linear change. A constant rate of change (gallons per minute) creates linear change.

Flashcard 93: Which option is a constant percent rate: "adds $10$ each week" or "increases by $10\%$ each week"?

Answer: "Increases by $10\%$ each week". Percentage increase indicates exponential change, not constant addition.

Flashcard 94: What is the percent rate for a common ratio of $0.75$ per interval?

Answer: $25\%$ decrease. Ratio $0.75 = 1 - 0.25$, so the decrease is $25\%$.

Flashcard 95: Which option is a constant percent rate: "adds $10$ each week" or "increases by $10\%$ each week"?

Answer: "Increases by $10\%$ each week". Percentage increase indicates exponential change, not constant addition.