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.

Front

How do you calculate the average rate of change of a function?

Back

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

Front

What is the average rate of change from day 5 to day 20 if f(5) = 1283 and f(20) = 1200?

Back

The average rate of change is \( \frac{1200 - 1283}{20 - 5} = \frac{-83}{15} \approx -5.53 \) decks per day.

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

What is the average rate of change from day 0 to day 5 if f(0) = 2000 and f(5) = 1283?

Back

The average rate of change is \( \frac{1283 - 2000}{5 - 0} = \frac{-717}{5} = -143.4 \) decks per day.

Front

What does it mean if the average rate of change is -143.4 decks per day?

Back

It means that, on average, the store lost 143.4 decks of trading cards each day over that period.

Front

What is the average rate of change between x = -1 and x = 0 if f(-1) = 1 and f(0) = -1?

Back

The average rate of change is \( \frac{-1 - 1}{0 - (-1)} = \frac{-2}{1} = -2 \).

Front

How do you interpret the average rate of change?

Back

The average rate of change can be interpreted as the change in the dependent variable per unit change in the independent variable over a specified interval.

Front

What is the average rate of change from day 15 to day 20 if f(15) = 1000 and f(20) = 962?

Back

The average rate of change is \( \frac{962 - 1000}{20 - 15} = \frac{-38}{5} = -7.6 \) decks per day.