Exponential Growth & 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 general formula for exponential growth?

Back

y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What is the general formula for exponential decay?

Back

y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

Front

If a quantity increases by 35% each year, what is the growth factor?

Back

The growth factor is 1.35.

Front

If a quantity decreases by 50% each year, what is the decay factor?

Back

The decay factor is 0.50.

Front

How do you calculate the value of an investment after 'n' years with exponential growth?

Back

Use the formula: Future Value = Initial Amount * (1 + growth rate)^n.

Front

How do you calculate the value of an asset after 'n' years with exponential decay?

Back

Use the formula: Future Value = Initial Amount * (1 - decay rate)^n.

Front

What is the initial amount in the function y = 15(1.35)^x?

Back

The initial amount is $15.

Front

What does the variable 'x' represent in exponential functions?

Back

The variable 'x' represents the time period, usually in years.