Exponential: Growth and Decay
Flashcard
•
Mathematics
•
8th - 10th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.
2.
FLASHCARD QUESTION
Front
What does the y-intercept of an exponential function represent?
Back
The y-intercept of an exponential function is the value of 'y' when 'x' is 0. It represents the initial value of the function.
Tags
CCSS.HSF-IF.C.7E
3.
FLASHCARD QUESTION
Front
How do you find the y-intercept of the function y = 1.25(5^x)?
Back
To find the y-intercept, substitute x = 0 into the function: y = 1.25(5^0) = 1.25.
Tags
CCSS.HSF-IF.C.7E
4.
FLASHCARD QUESTION
Front
What is the rate of growth in the function y = 5(1.27^x)?
Back
The rate of growth is the percentage increase represented by the base of the exponent. In this case, it is 27%.
Tags
CCSS.HSF-IF.C.8B
5.
FLASHCARD QUESTION
Front
What is the formula for calculating the future value of an investment with exponential growth?
Back
The formula is A = P(1 + r)^t, where A is the amount of money accumulated after n years, P is the principal amount, r is the rate of interest, and t is the time in years.
6.
FLASHCARD QUESTION
Front
What does the rate of decay in an exponential function indicate?
Back
The rate of decay indicates the percentage decrease in value over a specific time period, represented by the base of the exponent in a decay function.
Tags
CCSS.HSF-IF.C.8B
7.
FLASHCARD QUESTION
Front
How do you find the rate of decay in the function y = 35(0.65^x)?
Back
The rate of decay is calculated as (1 - base) * 100%. Here, it is (1 - 0.65) * 100% = 35%.
Tags
CCSS.HSF-IF.C.8B
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