Exponential Growth or Decay?

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to a rapid increase. For example, if a population doubles every year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time. For example, if a radioactive substance loses half of its mass every year, it is experiencing exponential decay.

Front

Identify the general form of an exponential growth equation.

Back

The general form is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

Identify the general form of an exponential decay equation.

Back

The general form is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What does the base of an exponential function represent?

Back

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

Front

How can you determine if a table represents exponential growth or decay?

Back

If the values in the table increase by a consistent percentage, it represents exponential growth. If they decrease by a consistent percentage, it represents exponential decay.

Front

What is the effect of a negative growth rate in an exponential function?

Back

A negative growth rate indicates exponential decay, meaning the quantity decreases over time.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value (a) represents the starting amount before any growth or decay occurs.

Front

How does compounding affect exponential growth?

Back

Compounding increases the amount of growth in exponential functions, as the growth builds on itself over time.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.