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Questions and Answers
What is the multiplicative rate of change of the function represented in the table?
What is the multiplicative rate of change of the function represented in the table?
2/3
Which function represents the frog population after x years if it is decreasing at an average rate of 3% per year?
Which function represents the frog population after x years if it is decreasing at an average rate of 3% per year?
f(x) = 1,200(0.97)^x
Which graph represents g(x) if it is the reflection of f(x) = 2^x over the y-axis?
Which graph represents g(x) if it is the reflection of f(x) = 2^x over the y-axis?
Graph 2
Which graph represents Chelsea's initial step in graphing the function f(x) = 20(1/4)^x?
Which graph represents Chelsea's initial step in graphing the function f(x) = 20(1/4)^x?
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What is the multiplicative rate of change for the exponential function f(x) = 2(5/2)^-x?
What is the multiplicative rate of change for the exponential function f(x) = 2(5/2)^-x?
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Which is an example of an exponential decay function?
Which is an example of an exponential decay function?
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Which graph represents the function f(x) = 100(0.7)^x?
Which graph represents the function f(x) = 100(0.7)^x?
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What best describes the graph of the function representing the number of live bacteria after x days of treatment if 40% remains alive?
What best describes the graph of the function representing the number of live bacteria after x days of treatment if 40% remains alive?
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What conclusion can be drawn about the functions f(x) and g(x) based on the table?
What conclusion can be drawn about the functions f(x) and g(x) based on the table?
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Which function represents the value of a car that depreciates by 15% each year if it was bought for $20,000?
Which function represents the value of a car that depreciates by 15% each year if it was bought for $20,000?
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Study Notes
Exponential Decay Functions Study Notes
- Exponential functions can exhibit multiplicative rates of change, such as a function with a rate of change calculated as 2/3.
- A frog population of 1,200 decreasing at 3% per year is modeled by the function f(x) = 1,200(0.97)^x.
- Graphs can represent exponential decay, with g(x) = (1/2)^x being a reflection of f(x) = 2^x over the y-axis.
- Plotting the initial value of a function like f(x) = 20(1/4)^x involves marking the point (0, 20) on the graph.
- The function f(x) = 2(5/2)^-x has a multiplicative rate of change of 0.4, indicating a decline over time.
- An example of an exponential decay function is represented by f(x) = 1/3(-9/2).
- The graph depicting f(x) = 100(0.7)^x shows a clear decline characteristic of exponential decay.
- A bacteria sample that starts at 5,000 alive and retains 40% each day can be modeled by f(x) = 5000(0.4)^x, displaying a horizontal asymptote at y = 0.
- Comparisons of two exponential functions reveal that reflections over the y-axis represent their relationship, such as between f(x) and g(x).
- The depreciation of a car valued at $20,000 at a rate of 15% per year is represented by the function f(x) = 20,000(0.85)^x, demonstrating typical exponential decay in asset value over time.
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Description
Test your knowledge about exponential decay functions with this quiz. It covers topics like multiplicative rates of change and modeling population decline. Perfect for understanding real-world applications of exponential functions.
