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Questions and Answers
Does the table represent an exponential function?
Does the table represent an exponential function?
False
How many crickets will there be after 2 years if a population of 160 crickets doubles in size every month?
How many crickets will there be after 2 years if a population of 160 crickets doubles in size every month?
2,684,354,560
How much is the investment worth after 2 decades if it starts at $2,300 and doubles in value every decade?
How much is the investment worth after 2 decades if it starts at $2,300 and doubles in value every decade?
$9,200
What is the graph of the function Y = 2 * 2^x?
What is the graph of the function Y = 2 * 2^x?
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What is the graph of the function Y = -2 * 5^x?
What is the graph of the function Y = -2 * 5^x?
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Study Notes
Exponential Functions Overview
- Exponential functions demonstrate rapid growth or decay, characterized by a constant percentage change.
- Common forms include f(x) = a * b^x, where 'a' is the initial value and 'b' is the growth factor.
Table Interpretation
- A given table with values X: 1, 2, 3, 4 and Y: -1, -8, -27, -64 does not represent an exponential function due to non-consistent relative growth between points.
Population Growth Example
- A population of 160 crickets with a monthly doubling rate is modeled by f(x) = 160 * 2^x.
- After 2 years (24 months), the cricket population will reach approximately 2,684,354,560.
Investment Growth Example
- An investment of $2,300 that doubles every decade is represented by f(x) = 2,300 * 2^x.
- After 2 decades, the investment value will grow to $9,200.
Graph Behavior Characteristics
- The graph of the function Y = 2 * 2^x exhibits an upward growth pattern, depicted as option B (↗︎).
- For the function Y = -2 * 5^x, the graph shows a downward decline, represented as option C (↘︎).
Visual Representation of Exponential Functions
- Understanding the direction of the graph (increasing or decreasing) is crucial for analyzing the behavior of exponential functions.
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Description
Test your knowledge of exponential functions through these flashcards. Each card provides common scenarios and definitions related to exponential growth and decay. Perfect for students looking to strengthen their understanding in this area of mathematics.
