Exponential Functions Flashcard Review

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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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 f(x) = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent. It represents growth or decay processes.
2.
FLASHCARD QUESTION
Front
What does the base 'b' represent in an exponential function?
Back
The base 'b' in an exponential function represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the function.
3.
FLASHCARD QUESTION
Front
How do you determine the initial amount in an exponential function?
Back
The initial amount 'a' in an exponential function f(x) = a(b^x) is the value of the function when x = 0.
4.
FLASHCARD QUESTION
Front
If a savings account has an annual interest rate of 5%, what is the exponential function?
Back
f(x) = P(1.05)^x, where P is the initial amount.
5.
FLASHCARD QUESTION
Front
What is the formula to calculate the future value of an investment using exponential growth?
Back
Future Value = Present Value * (1 + r)^t, where r is the growth rate and t is the time in years.
6.
FLASHCARD QUESTION
Front
What is the growth rate if a population increases by 20% each year?
Back
The growth rate is 20%.
7.
FLASHCARD QUESTION
Front
How do you convert a percentage increase to a growth factor?
Back
To convert a percentage increase to a growth factor, use the formula: Growth Factor = 1 + (percentage increase / 100). For example, a 15% increase becomes 1.15.
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