Exponential Growth and Decay

Front

What is Exponential Growth?

Back

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

Front

What is Exponential Decay?

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 formula for Exponential Growth?

Back

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

Front

What is the formula for Exponential Decay?

Back

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

Front

What does the initial value represent in an exponential function?

Back

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

Front

How can you identify Exponential Growth from a table of values?

Back

In Exponential Growth, the values increase rapidly and the ratio of consecutive values remains constant.

Front

How can you identify Exponential Decay from a table of values?

Back

In Exponential Decay, the values decrease rapidly and the ratio of consecutive values remains constant.

Front

What is a common example of Exponential Growth in real life?

Back

A common example is population growth, where the population increases at a rate proportional to its current size.

Front

What is a common example of Exponential Decay in real life?

Back

A common example is radioactive decay, where the quantity of a radioactive substance decreases over time.

Front

What is the difference between Linear Growth and Exponential Growth?

Back

Linear Growth increases by a constant amount, while Exponential Growth increases by a constant percentage.