Exponential Functions Flashcards

Questions and Answers

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?

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?

$9,200

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?

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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.

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.