Exponential Decay Functions Quiz

Questions and Answers

Which function represents exponential decay?

f(x) = 3x

f(x) = 2(2/3)x (correct)

f(x) = 4(1/2)x

f(x) = 2(3/2)x

Which graph represents exponential decay?

Graph B

Graph D (correct)

Graph C

Graph A

In order for the table to show exponential decay, what must the value of d be?

Which statements describe the function f(x) = 3()x? Check all that apply.

The range of the function is all real numbers greater than 0. Signup and view all the answers

Which function represents the given graph?

f(x) = 100 · (3/5)x Signup and view all the answers

Which graph represents the function f(x) = (3/2)-x?

Graph B Signup and view all the answers

What values should the doctor use for a and b in the exponential function for bone density?

a = 1,500, b = 0.97 Signup and view all the answers

If the bee population is decreasing at a rate of 5% per year, which statements about the situation are true? Check all that apply.

The range values, in the context, are limited to whole numbers. Signup and view all the answers

How do the graphs of the functions f(x) = (3/2)x and g(x) = (2/3)x compare?

The graphs are reflections of each other over the y-axis, with g(x) showing exponential decay and f(x) showing exponential growth. Signup and view all the answers

Study Notes

Exponential Decay Functions

Exponential decay functions have a base between 0 and 1. Example function: f(x) = 2(2/3)x.
Identifying exponential decay graphically involves looking for curves that decrease rapidly over time.

Key Values for Decay Functions

For a table to indicate exponential decay, specific parameters must be set. Example value: d must be 18.

Function Characteristics

For the function f(x) = 3()x:
- Each output reduces to one-third of the previous output, indicating decay.
- As inputs increase, outputs decrease in value.
- The function's graph is not linear but decreasing.
- The range includes all real numbers greater than 0, while the domain includes all real numbers.

Specific Functions and Applications

A function representing a graph of exponential decay can be formulated as f(x) = 100 · (3/5)x.
The decay function f(x) = (3/2)-x exemplifies exponential decay.

Real-World Applications

In medicine, a patient's annual bone density loss of 3% can be expressed as f(x) = 1,500(0.97)x, where initial density is 1,500 kg/mg3.
In agriculture, a bee population of 9,000 decreasing at a rate of 5% per year can be modeled by f(x) = 9,000(0.95)x.
- After two years, an estimated population of approximately 8,120 bees remains.
- Domain values only account for whole numbers, reflecting reality in bee count.

Comparative Analysis

The functions f(x) = (3/2)x and g(x) = (2/3)x are reflections over the y-axis with:
- g(x) representing exponential decay.
- f(x) showcasing exponential growth.
- Both have the same initial value, emphasizing their relationship.

Description

This quiz focuses on understanding exponential decay functions, their characteristics, and their real-world applications. You will learn how to identify these functions graphically and interpret specific parameters that indicate decay. Test your knowledge with examples and applications in various contexts!