Exponential Growth & Decay

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+3
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is exponential growth?
Back
Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate. It can be represented by the formula y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.
Tags
CCSS.HSF-LE.A.1A
2.
FLASHCARD QUESTION
Front
What is exponential decay?
Back
Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline. It can be represented by the formula y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.
Tags
CCSS.HSF-IF.C.8B
3.
FLASHCARD QUESTION
Front
What is the formula for exponential growth?
Back
The formula for exponential growth is y = a(1 + r)^t, where 'y' is the final amount, 'a' is the initial amount, 'r' is the growth rate (as a decimal), and 't' is the time period.
Tags
CCSS.HSF-IF.C.8B
4.
FLASHCARD QUESTION
Front
What is the formula for exponential decay?
Back
The formula for exponential decay is y = a(1 - r)^t, where 'y' is the final amount, 'a' is the initial amount, 'r' is the decay rate (as a decimal), and 't' is the time period.
Tags
CCSS.HSF-IF.C.8B
5.
FLASHCARD QUESTION
Front
How do you calculate the value of an investment after a certain number of years with exponential growth?
Back
To calculate the value of an investment after a certain number of years with exponential growth, use the formula y = a(1 + r)^t, substituting 'a' with the initial investment, 'r' with the annual growth rate, and 't' with the number of years.
6.
FLASHCARD QUESTION
Front
How do you calculate the value of an investment after a certain number of years with exponential decay?
Back
To calculate the value of an investment after a certain number of years with exponential decay, use the formula y = a(1 - r)^t, substituting 'a' with the initial investment, 'r' with the annual decay rate, and 't' with the number of years.
7.
FLASHCARD QUESTION
Front
What does a decay rate of 10% mean in terms of exponential decay?
Back
A decay rate of 10% means that each year, the quantity decreases to 90% of its value from the previous year. This can be represented by the formula y = a(0.90)^t.
Tags
CCSS.HSF-IF.C.8B
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