Exponential Growth and Decay Graphing

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 describes the process of reducing an amount by a consistent percentage rate over a period of time, resulting in a decrease that slows down as the quantity diminishes.

Front

What is the general formula for exponential growth?

Back

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

Front

What is the general formula for exponential decay?

Back

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

Front

How do you convert a percentage to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 14.9% becomes 0.149.

Front

What does the term 'half-life' refer to in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in contexts like radioactive decay.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive values, indicating multiplicative growth or decay.

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

If a population decreases by 1.5% per year, what is the decay rate in decimal form?

Back

The decay rate in decimal form is 0.015.