Exponential Growth and Decay
Flashcard
•
Mathematics
•
9th Grade
•
Practice Problem
•
Hard
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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 over time.
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 that slows over time.
3.
FLASHCARD QUESTION
Front
What does the initial value represent in an exponential function?
Back
The initial value is the starting amount before any growth or decay occurs, often represented as 'a' in the function y = a(b)^x.
4.
FLASHCARD QUESTION
Front
In the function y = 5000(0.98)^x, what does 0.98 represent?
Back
0.98 represents the decay factor, indicating that the amount decreases by 2% each year.
5.
FLASHCARD QUESTION
Front
How do you convert a percentage decrease to a decay factor?
Back
To convert a percentage decrease to a decay factor, subtract the percentage (as a decimal) from 1. For example, a 14.9% decrease becomes 1 - 0.149 = 0.851.
6.
FLASHCARD QUESTION
Front
What is the formula for exponential growth?
Back
The formula for exponential growth is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.
7.
FLASHCARD QUESTION
Front
What is the formula for exponential decay?
Back
The formula for exponential decay is f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.
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