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 refers to the process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease 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 future value in exponential growth?

Back

Multiply the initial value by (1 + growth rate) raised to the power of time.

Front

How do you calculate the future value in exponential decay?

Back

Multiply the initial value by (1 - decay rate) raised to the power of time.

Front

If a population of 1000 increases by 20% per year, what will it be after 1 year?

Back

1200 (1000 * 1.20).

Front

If a population of 1000 decreases by 10% per year, what will it be after 1 year?

Back

900 (1000 * 0.90).

Front

What is the significance of the base 'e' in exponential functions?

Back

The base 'e' (approximately 2.718) is used in continuous growth and decay models, representing natural growth processes.

Front

What is a real-world example of exponential growth?

Back

The spread of a virus can exhibit exponential growth as each infected person can infect multiple others.