Linear & Exponential Growth - SAT Math
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Compare growth rates: linear vs. exponential.
Compare growth rates: linear vs. exponential.
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Exponential functions grow faster than linear ones for large $x$.
Exponential functions grow faster than linear ones for large $x$.
General exponential decay model.
General exponential decay model.
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$y = a(1 - r)^t$.
$y = a(1 - r)^t$.
General exponential growth model.
General exponential growth model.
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$y = a(1 + r)^t$.
$y = a(1 + r)^t$.
How can you tell if data represent exponential growth?
How can you tell if data represent exponential growth?
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Equal ratios in $y$ for equal intervals in $x$.
Equal ratios in $y$ for equal intervals in $x$.
How can you tell if data represent linear growth?
How can you tell if data represent linear growth?
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Equal differences in $y$ for equal intervals in $x$.
Equal differences in $y$ for equal intervals in $x$.
If $y = 100(0.9)^t$, what is decay rate?
If $y = 100(0.9)^t$, what is decay rate?
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10% per time period.
10% per time period.
If $y = 100(1.1)^t$, what is growth rate?
If $y = 100(1.1)^t$, what is growth rate?
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10% per time period.
10% per time period.
If a bacteria population doubles every 4 hours, write the model $N = a(2)^{t/4}$. What does $a$ represent?
If a bacteria population doubles every 4 hours, write the model $N = a(2)^{t/4}$. What does $a$ represent?
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The initial number of bacteria.
The initial number of bacteria.
Write an equation for:
'A city’s population doubles every 12 years from 50,000.'
Write an equation for:
'A city’s population doubles every 12 years from 50,000.'
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$P = 50000(2)^{t/12}$.
$P = 50000(2)^{t/12}$.