Recognize Percent Growth or Decay - Algebra 2
Card 1 of 30
Find the multiplier for “value halves every $6$ hours” per hour.
Find the multiplier for “value halves every $6$ hours” per hour.
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$\left(\frac{1}{2}\right)^{\frac{1}{6}}$. Per-hour multiplier is the sixth root of $\frac{1}{2}$.
$\left(\frac{1}{2}\right)^{\frac{1}{6}}$. Per-hour multiplier is the sixth root of $\frac{1}{2}$.
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Choose the model with constant percent change: $y=400\cdot(0.9)^t$ or $y=400-0.9t$.
Choose the model with constant percent change: $y=400\cdot(0.9)^t$ or $y=400-0.9t$.
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$y=400\cdot(0.9)^t$. Exponential form with base indicates percent change.
$y=400\cdot(0.9)^t$. Exponential form with base indicates percent change.
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What is the common ratio if values go $80,\ 88,\ 96.8$ at equal time steps?
What is the common ratio if values go $80,\ 88,\ 96.8$ at equal time steps?
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$1.1$. Divide consecutive terms: $\frac{88}{80} = \frac{96.8}{88} = 1.1$.
$1.1$. Divide consecutive terms: $\frac{88}{80} = \frac{96.8}{88} = 1.1$.
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What type of change is indicated by “increases by $5%$ each month”?
What type of change is indicated by “increases by $5%$ each month”?
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Constant percent growth (exponential growth). Percent change per unit time indicates exponential growth.
Constant percent growth (exponential growth). Percent change per unit time indicates exponential growth.
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What type of change is indicated by “decreases by $12%$ per year”?
What type of change is indicated by “decreases by $12%$ per year”?
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Constant percent decay (exponential decay). Percent change per unit time indicates exponential decay.
Constant percent decay (exponential decay). Percent change per unit time indicates exponential decay.
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What is the growth factor for a constant increase of $r%$ per interval?
What is the growth factor for a constant increase of $r%$ per interval?
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$1+\frac{r}{100}$. Add the percent rate as a decimal to 1.
$1+\frac{r}{100}$. Add the percent rate as a decimal to 1.
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What is the decay factor for a constant decrease of $r%$ per interval?
What is the decay factor for a constant decrease of $r%$ per interval?
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$1-\frac{r}{100}$. Subtract the percent rate as a decimal from 1.
$1-\frac{r}{100}$. Subtract the percent rate as a decimal from 1.
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What is the exponential form for percent growth or decay over $t$ intervals?
What is the exponential form for percent growth or decay over $t$ intervals?
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$A(t)=A_0\cdot b^t$. Standard exponential model with base $b$ and time $t$.
$A(t)=A_0\cdot b^t$. Standard exponential model with base $b$ and time $t$.
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What condition on $b$ indicates exponential growth in $A(t)=A_0\cdot b^t$?
What condition on $b$ indicates exponential growth in $A(t)=A_0\cdot b^t$?
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$b>1$. Base greater than 1 means the quantity increases.
$b>1$. Base greater than 1 means the quantity increases.
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What condition on $b$ indicates exponential decay in $A(t)=A_0\cdot b^t$?
What condition on $b$ indicates exponential decay in $A(t)=A_0\cdot b^t$?
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$0<b<1$. Base between 0 and 1 means the quantity decreases.
$0<b<1$. Base between 0 and 1 means the quantity decreases.
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What phrase signals linear (not percent) change: “adds $15$ each week” or “multiplies by $1.15$ each week”?
What phrase signals linear (not percent) change: “adds $15$ each week” or “multiplies by $1.15$ each week”?
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Adds $15$ each week (linear). Fixed amount added signals linear, not exponential change.
Adds $15$ each week (linear). Fixed amount added signals linear, not exponential change.
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Which phrase signals constant percent change: “decreases by $30$ each year” or “decreases by $30%$ each year”?
Which phrase signals constant percent change: “decreases by $30$ each year” or “decreases by $30%$ each year”?
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Decreases by $30%$ each year. Percent change indicates exponential, not linear growth.
Decreases by $30%$ each year. Percent change indicates exponential, not linear growth.
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What is the percent rate per interval if the multiplier each interval is $1.08$?
What is the percent rate per interval if the multiplier each interval is $1.08$?
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$8%$ growth per interval. Subtract 1 from the multiplier and convert to percent.
$8%$ growth per interval. Subtract 1 from the multiplier and convert to percent.
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What is the percent rate per interval if the multiplier each interval is $0.93$?
What is the percent rate per interval if the multiplier each interval is $0.93$?
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$7%$ decay per interval. Subtract the multiplier from 1 and convert to percent.
$7%$ decay per interval. Subtract the multiplier from 1 and convert to percent.
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What is the multiplier for “grows by $3.5%$ per day”?
What is the multiplier for “grows by $3.5%$ per day”?
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$1.035$. Add the percent rate as a decimal to 1.
$1.035$. Add the percent rate as a decimal to 1.
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What is the multiplier for “decays by $18%$ per hour”?
What is the multiplier for “decays by $18%$ per hour”?
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$0.82$. Subtract the percent rate as a decimal from 1.
$0.82$. Subtract the percent rate as a decimal from 1.
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Identify the model type for $P(t)=120\cdot(0.6)^t$.
Identify the model type for $P(t)=120\cdot(0.6)^t$.
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Exponential decay. Base $0.6 < 1$ indicates exponential decay.
Exponential decay. Base $0.6 < 1$ indicates exponential decay.
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Identify the model type for $N(t)=50\cdot(1.2)^t$.
Identify the model type for $N(t)=50\cdot(1.2)^t$.
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Exponential growth. Base $1.2 > 1$ indicates exponential growth.
Exponential growth. Base $1.2 > 1$ indicates exponential growth.
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What is the per-interval percent change for $A(t)=A_0\cdot(1.15)^t$?
What is the per-interval percent change for $A(t)=A_0\cdot(1.15)^t$?
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$15%$ growth per interval. Base $1.15$ means $15%$ growth per interval.
$15%$ growth per interval. Base $1.15$ means $15%$ growth per interval.
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What is the per-interval percent change for $A(t)=A_0\cdot(0.72)^t$?
What is the per-interval percent change for $A(t)=A_0\cdot(0.72)^t$?
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$28%$ decay per interval. Base $0.72$ means $28%$ decay per interval.
$28%$ decay per interval. Base $0.72$ means $28%$ decay per interval.
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Which situation is constant percent change: “$10%$ interest yearly” or “$10$ dollars interest yearly”?
Which situation is constant percent change: “$10%$ interest yearly” or “$10$ dollars interest yearly”?
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$10%$ interest yearly. Percent interest indicates exponential compound growth.
$10%$ interest yearly. Percent interest indicates exponential compound growth.
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Which situation is constant percent change: “value drops $200$ per year” or “value drops $20%$ per year”?
Which situation is constant percent change: “value drops $200$ per year” or “value drops $20%$ per year”?
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Value drops $20%$ per year. Percent change indicates exponential, not linear decay.
Value drops $20%$ per year. Percent change indicates exponential, not linear decay.
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What is the multiplier for “increases by $25%$ per interval”?
What is the multiplier for “increases by $25%$ per interval”?
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$1.25$. Add the percent rate as a decimal to 1.
$1.25$. Add the percent rate as a decimal to 1.
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What is the multiplier for “decreases by $25%$ per interval”?
What is the multiplier for “decreases by $25%$ per interval”?
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$0.75$. Subtract the percent rate as a decimal from 1.
$0.75$. Subtract the percent rate as a decimal from 1.
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Identify whether $A(t+1)=1.04,A(t)$ represents growth or decay.
Identify whether $A(t+1)=1.04,A(t)$ represents growth or decay.
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Growth. Multiplier $1.04 > 1$ indicates exponential growth.
Growth. Multiplier $1.04 > 1$ indicates exponential growth.
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Identify whether $A(t+1)=0.97,A(t)$ represents growth or decay.
Identify whether $A(t+1)=0.97,A(t)$ represents growth or decay.
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Decay. Multiplier $0.97 < 1$ indicates exponential decay.
Decay. Multiplier $0.97 < 1$ indicates exponential decay.
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What is the percent rate per interval if $A(t+1)=1.005,A(t)$?
What is the percent rate per interval if $A(t+1)=1.005,A(t)$?
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$0.5%$ growth per interval. Subtract 1 from multiplier and convert to percent.
$0.5%$ growth per interval. Subtract 1 from multiplier and convert to percent.
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What is the percent rate per interval if $A(t+1)=0.995,A(t)$?
What is the percent rate per interval if $A(t+1)=0.995,A(t)$?
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$0.5%$ decay per interval. Subtract multiplier from 1 and convert to percent.
$0.5%$ decay per interval. Subtract multiplier from 1 and convert to percent.
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Which description matches $b=1$ in $A(t)=A_0\cdot b^t$?
Which description matches $b=1$ in $A(t)=A_0\cdot b^t$?
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No change (constant value). Base equals 1 means no growth or decay occurs.
No change (constant value). Base equals 1 means no growth or decay occurs.
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Which is the correct base $b$ for “decays by $9%$ per interval” in $A(t)=A_0\cdot b^t$?
Which is the correct base $b$ for “decays by $9%$ per interval” in $A(t)=A_0\cdot b^t$?
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$b=0.91$. Subtract decay rate from 1: $1 - 0.09 = 0.91$.
$b=0.91$. Subtract decay rate from 1: $1 - 0.09 = 0.91$.
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