Growth, Decay, Double Time, and Half Life

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in 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 fixed percentage over a period of time. For example, radioactive substances decay at a rate proportional to their current amount.

Front

Define double time in the context of exponential growth.

Back

Double time is the period it takes for a quantity undergoing exponential growth to double in size. It can be calculated using the formula: Double Time = ln(2) / growth rate.

Front

Define half-life in the context of exponential decay.

Back

Half-life is the time required for a quantity undergoing exponential decay to reduce to half its initial amount. It is commonly used in radioactive decay and can be calculated using the formula: Half-life = ln(2) / decay rate.

Front

What is the general form of an exponential growth function?

Back

Front

What is the general form of an exponential decay function?

Back

Front

How do you determine if a function represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What is the function for a population that doubles every hour starting with 4 individuals?

Back

Front

If a quantity decreases by 50% each hour, what is the function to represent this decay?

Back

Front

What is the relationship between growth rate and double time?

Back

The growth rate is inversely related to double time; a higher growth rate results in a shorter double time.