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Questions and Answers
Which function represents exponential decay?
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?
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?
In order for the table to show exponential decay, what must the value of d be?
18
Which statements describe the function f(x) = 3()x? Check all that apply.
Which statements describe the function f(x) = 3()x? Check all that apply.
Which function represents the given graph?
Which function represents the given graph?
Which graph represents the function f(x) = (3/2)-x?
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?
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.
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?
How do the graphs of the functions f(x) = (3/2)x and g(x) = (2/3)x compare?
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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.
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