
A6 - Exponential Growth and Decay Word Problems
Flashcard
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What is exponential decay?
Back
Exponential decay is a process where a quantity decreases at a rate proportional to its current value, often modeled by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.
2.
FLASHCARD QUESTION
Front
How do you model exponential growth?
Back
Exponential growth can be modeled by the equation y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.
3.
FLASHCARD QUESTION
Front
What is the formula for calculating the remaining amount after exponential decay?
Back
The formula is A = A0 * e^(-kt), where A0 is the initial amount, k is the decay constant, and t is time.
4.
FLASHCARD QUESTION
Front
If a population grows by 5% each year, what is the growth factor?
Back
The growth factor is 1.05.
5.
FLASHCARD QUESTION
Front
What does a decay rate of 50% mean in terms of value after one year?
Back
It means that after one year, the value will be half of the original value.
6.
FLASHCARD QUESTION
Front
How do you find the time it takes for an investment to double at a constant growth rate?
Back
You can use the Rule of 70: Time (years) = 70 / growth rate (percentage).
7.
FLASHCARD QUESTION
Front
What is the significance of the base 'e' in exponential functions?
Back
The base 'e' (approximately 2.718) is the natural base used in continuous growth or decay models.
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