Word Problems - SAT Math
Card 0 of 45
General form of a linear model.
General form of a linear model.
$y = mx + b$.
$y = mx + b$.
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In $y = mx + b$, what does $m$ represent?
In $y = mx + b$, what does $m$ represent?
The rate of change or slope (change in $y$ per unit change in $x$).
The rate of change or slope (change in $y$ per unit change in $x$).
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In $y = mx + b$, what does $b$ represent?
In $y = mx + b$, what does $b$ represent?
The initial value or $y$-intercept.
The initial value or $y$-intercept.
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If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
If a car travels 60 miles per hour, what is the linear model for distance $d$ in miles after $t$ hours?
$d = 60t$.
$d = 60t$.
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If a phone plan costs $20$ per month plus a $30$ activation fee, write a linear cost model.
If a phone plan costs $20$ per month plus a $30$ activation fee, write a linear cost model.
$C = 20m + 30$.
$C = 20m + 30$.
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A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
A candle burns at 2 cm per hour from an initial height of 10 cm. Write the model.
$h = 10 - 2t$.
$h = 10 - 2t$.
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If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
If a worker earns $15 per hour plus $50 bonus, write earnings model $E$ after $h$ hours.
$E = 15h + 50$.
$E = 15h + 50$.
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If $y = 5x + 2$, find the rate of change and initial value.
If $y = 5x + 2$, find the rate of change and initial value.
Rate = 5, initial value = 2.
Rate = 5, initial value = 2.
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If the population increases by 200 each year from 5,000, write the linear model.
If the population increases by 200 each year from 5,000, write the linear model.
$P = 5000 + 200t$.
$P = 5000 + 200t$.
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What does it mean if slope $m$ is negative in $y = mx + b$?
What does it mean if slope $m$ is negative in $y = mx + b$?
The quantity decreases at a constant rate.
The quantity decreases at a constant rate.
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General exponential growth model.
General exponential growth model.
$y = a(1 + r)^t$.
$y = a(1 + r)^t$.
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General exponential decay model.
General exponential decay model.
$y = a(1 - r)^t$.
$y = a(1 - r)^t$.
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In $y = a(1 + r)^t$, what does $a$ represent?
In $y = a(1 + r)^t$, what does $a$ represent?
The initial amount (value at $t = 0$).
The initial amount (value at $t = 0$).
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In $y = a(1 + r)^t$, what does $r$ represent?
In $y = a(1 + r)^t$, what does $r$ represent?
The rate of growth per time period (in decimal form).
The rate of growth per time period (in decimal form).
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In $y = a(1 + r)^t$, what does $t$ represent?
In $y = a(1 + r)^t$, what does $t$ represent?
The number of time periods.
The number of time periods.
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If an investment of $1000$ grows by 5% per year, write the model for value after $t$ years.
If an investment of $1000$ grows by 5% per year, write the model for value after $t$ years.
$V = 1000(1.05)^t$.
$V = 1000(1.05)^t$.
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If a population of 800 declines 3% per year, write the decay model.
If a population of 800 declines 3% per year, write the decay model.
$P = 800(0.97)^t$.
$P = 800(0.97)^t$.
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Identify growth or decay: $y = 500(1.02)^t$.
Identify growth or decay: $y = 500(1.02)^t$.
Growth (since base > 1).
Growth (since base > 1).
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Identify growth or decay: $y = 200(0.85)^t$.
Identify growth or decay: $y = 200(0.85)^t$.
Decay (since base < 1).
Decay (since base < 1).
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If $y = 100(1.1)^t$, what is growth rate?
If $y = 100(1.1)^t$, what is growth rate?
10% per time period.
10% per time period.
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