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. For example, if a population grows by 20% each year, it will grow faster each subsequent year.

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. For example, if a substance loses 10% of its mass each hour, it will lose more mass each subsequent hour.

Front

How do you identify exponential growth in an equation?

Back

In an equation, exponential growth is identified by a base greater than 1, such as A = P(1 + r)^t, where r is the growth rate.

Front

How do you identify exponential decay in an equation?

Back

In an equation, exponential decay is identified by a base less than 1, such as A = P(1 - r)^t, where r is the decay rate.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

If a population of 1000 increases by 50% each year, what will be the population after 1 year?

Back

Population after 1 year = 1000(1 + 0.50)^1 = 1500.

Front

If a substance has a half-life of 3 years, how much of a 100g sample remains after 6 years?

Back

After 6 years, 100g will decay to 25g, as it halves every 3 years.

Front

What does the term 'initial amount' refer to in exponential functions?

Back

The initial amount refers to the starting value before any growth or decay occurs, represented by P in the formulas.

Front

What is the significance of the growth rate in exponential functions?

Back

The growth rate determines how quickly the quantity increases in exponential growth or decreases in exponential decay.