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, leading to rapid increases as time progresses.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a consistent percentage rate over time, resulting in a rapid decline initially that slows down over time.

Front

Define the growth factor in exponential growth.

Back

The growth factor is calculated as (1 + r), where r is the growth rate expressed as a decimal.

Front

Define the decay factor in exponential decay.

Back

The decay factor is calculated as (1 - r), where r is the decay rate expressed as a decimal.

Front

If a population of 1,000 increases by 20% each month, what is the population after 1 month?

Back

1,000 * (1 + 0.20) = 1,200.

Front

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula: Future Value = Present Value * (1 + r)^t, where r is the growth rate and t is the time in periods.

Front

How do you calculate the present value of an investment with exponential decay?

Back

Use the formula: Present Value = Future Value / (1 + r)^t, where r is the decay rate and t is the time in periods.

Front

What is the formula for exponential decay of a car's value?

Back

Value = Initial Value * (1 - r)^t, where r is the depreciation rate and t is the number of years.

Front

If a culture of bacteria starts with 10,000 cells and dies at a rate of 25% per year, what is the equation representing this situation?

Back

y = 10,000(0.75)^x.

Front

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

Back

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