Average Rate of Change Exponential Functions

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Mathematics
•
9th Grade
•
Hard
+1
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1.
FLASHCARD QUESTION
Front
What is the average rate of change of a function over an interval?
Back
The average rate of change of a function over an interval [a, b] is calculated as (f(b) - f(a)) / (b - a). It represents the change in the function's value divided by the change in the input value.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
2.
FLASHCARD QUESTION
Front
How do you calculate the average rate of change for an exponential function?
Back
To calculate the average rate of change for an exponential function f(x) = a * b^x over an interval [c, d], use the formula: (f(d) - f(c)) / (d - c). Substitute the values of f(d) and f(c) using the exponential function.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
3.
FLASHCARD QUESTION
Front
What is an exponential function?
Back
An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent. The base b determines the growth or decay rate.
4.
FLASHCARD QUESTION
Front
What does it mean for a function to have a negative average rate of change?
Back
A negative average rate of change indicates that the function's value decreases over the specified interval. This means that as the input increases, the output decreases.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
5.
FLASHCARD QUESTION
Front
What is the significance of the base in an exponential function?
Back
The base in an exponential function determines the growth or decay rate. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.
Tags
CCSS.HSF-IF.C.8B
6.
FLASHCARD QUESTION
Front
How can you interpret the average rate of change in a real-world context?
Back
In a real-world context, the average rate of change can represent how a quantity changes over time, such as the depreciation of a car's value or the increase in population.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
7.
FLASHCARD QUESTION
Front
What is the average rate of change of the function f(x) = 3(2)^x from x = 1 to x = 5?
Back
To find the average rate of change, calculate f(5) and f(1): f(5) = 3(2)^5 = 96, f(1) = 3(2)^1 = 6. The average rate of change is (96 - 6) / (5 - 1) = 22.5.
Tags
CCSS.8.F.B.4
CCSS.HSF.IF.B.6
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