Key Features of Exponential Functions

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 the base (a positive real number), and 'x' is the exponent.

Front

What is the initial value in the function y = 6.87(4)^x?

Back

The initial value is 6.87.

Front

How can you identify if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'b' is a constant greater than 0 and not equal to 1.

Front

What is the range of an exponential function?

Back

The range of an exponential function is y > 0.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the function increases rapidly as 'x' increases, typically represented by a base 'b' greater than 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the function decreases rapidly as 'x' increases, typically represented by a base 'b' between 0 and 1.

Front

How do you write an exponential function from a table of values?

Back

To write an exponential function from a table, identify the initial value and the growth/decay factor, then express it in the form f(x) = a * b^x.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = A0 * (1 + r)^t, where A0 is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is A = A0 * (1 - r)^t, where A0 is the initial amount, r is the decay rate, and t is time.