Warm Up for Unit 3 Test
Flashcard
•
Mathematics
•
9th - 12th Grade
•
Practice Problem
•
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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.
2.
FLASHCARD QUESTION
Front
What is the difference between exponential growth and exponential decay?
Back
Exponential growth occurs when a quantity increases at a rate proportional to its current value (b > 1). Exponential decay occurs when a quantity decreases at a rate proportional to its current value (0 < b < 1).
3.
FLASHCARD QUESTION
Front
What is the general form of an exponential decay function?
Back
The general form is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.
4.
FLASHCARD QUESTION
Front
What is the decay rate in the function y = 1500(1 - 0.015)^t?
Back
The decay rate is 0.015, or 1.5% per year.
5.
FLASHCARD QUESTION
Front
How do you determine the amount left after a certain time in an exponential decay scenario?
Back
Use the formula y = a(1 - r)^t, substituting 'a' for the initial amount, 'r' for the decay rate, and 't' for time.
6.
FLASHCARD QUESTION
Front
What is the equation of a function that models exponential growth?
Back
An example is y = a(b^x) where b > 1, indicating that the quantity increases over time.
7.
FLASHCARD QUESTION
Front
What is the value of y when x = 2 in the function y = 32(1/4)^x?
Back
y = 32(1/4)^2 = 32(1/16) = 2.
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