Exponential Decay Functions Quiz

Which function represents exponential decay?

Which graph represents exponential decay?

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.

Which function represents the given graph?

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

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

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

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

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.

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!