Exponential Functions and Decay

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.

Front

What does exponential growth mean?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

Front

What does exponential decay mean?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

Front

What is the general form of an exponential growth function?

Back

f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Front

What is the general form of an exponential decay function?

Back

f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the range of an exponential function?

Back

The range of an exponential function is y > 0.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers.

Front

How do you identify exponential growth on a graph?

Back

Exponential growth is identified by a curve that rises steeply as x increases.

Front

How do you identify exponential decay on a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of f(0), which equals 'a'.