Questions and Answers
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?
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?
Graph 2
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?
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Which is an example of an exponential decay function?
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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?
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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?
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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.
