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 is the formula for exponential growth?

Back

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

Front

What is the formula for exponential decay?

Back

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

Front

How do you calculate the value of an asset after depreciation?

Back

Use the formula: Value = Initial Value × (1 - rate)^t, where 'rate' is the depreciation rate and 't' is the number of years.

Front

What does the term 'common ratio' mean in exponential functions?

Back

The common ratio is the factor by which a quantity multiplies during each time period in exponential growth or decay.

Front

If a population decreases by 6% per year, what is the growth factor?

Back

The growth factor is 1 - 0.06 = 0.94.

Front

How do you find the population after a certain number of years with exponential decay?

Back

Use the formula: Population = Initial Population × (1 - decay rate)^number of years.

Front

What is the significance of the base in an exponential function?

Back

The base indicates the growth or decay rate; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

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

Back

Divide the percentage by 100. For example, a 25% growth rate becomes 0.25.