Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What does the initial value represent in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, often represented as 'a' in the function y = a(1 + r)^x.

Front

In the function y = a(1 + r)^x, what does 'r' represent?

Back

'r' represents the rate of growth (if positive) or decay (if negative) expressed as a decimal.

Front

How do you convert a percentage increase to a decimal for use in exponential functions?

Back

To convert a percentage increase to a decimal, divide the percentage by 100. For example, a 35% increase becomes 0.35.

Front

How do you convert a percentage decrease to a decimal for use in exponential functions?

Back

To convert a percentage decrease to a decimal, divide the percentage by 100 and subtract from 1. For example, a 14.9% decrease becomes 1 - 0.149 = 0.851.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is y = 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

The general form of an exponential decay function is y = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80, calculated as 1 - 0.20.

Front

How do you write an exponential function for a quantity that doubles every year?

Back

The function is y = a(2)^x, where 'a' is the initial amount.