Exponential Functions - Average ROC

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. It describes growth or decay processes.

Front

What does ROC stand for in mathematics?

Back

ROC stands for Rate of Change, which measures how a quantity changes in relation to another quantity.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you calculate the average rate of change of a function over an interval [a, b]?

Back

The average rate of change is calculated using the formula: \( \frac{f(b) - f(a)}{b - a} \).

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CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change between x = -1 and x = 0 for the function f(x) = 2^x?

Back

The average rate of change is \( \frac{f(0) - f(-1)}{0 - (-1)} = \frac{1 - 0.5}{1} = 0.5 \).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a function f represents the number of trading cards, what does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the number of trading cards is decreasing over the specified interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change from day 5 to day 15 if f(5) = 528 and f(15) = 1283?

Back

The average rate of change is \( \frac{1283 - 528}{15 - 5} = \frac{755}{10} = 75.5 \).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does it mean if the average rate of change is -143.3 cards/day?

Back

It means that, on average, the store is losing 143.3 popular trading cards each day.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

How do you interpret the average rate of change in a real-world context?

Back

The average rate of change can be interpreted as the change in a quantity per unit of time or another variable, providing insight into trends over that interval.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the average rate of change of the function f(x) = 22000(0.9)^x between x = 0 and x = 4?

Back

The average rate of change is approximately -$1,891.45/year.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the significance of the base in an exponential function?

Back

The base determines the growth or decay rate of the function. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B