Exponential Growth and Decay Practice

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. Example: Population growth of bacteria.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, leading to a rapid decline over time. Example: Radioactive decay.

Front

Identify an example of exponential growth in the real world.

Back

Spread of a viral infection.

Front

Identify an example of exponential decay in the real world.

Back

Radioactive decay.

Front

What is a common characteristic of exponential growth?

Back

The growth rate increases as the quantity increases.

Front

What is a common characteristic of exponential decay?

Back

The decay rate decreases as the quantity decreases.

Front

How does population growth of a country exemplify exponential growth?

Back

As the population increases, the number of births typically increases, leading to faster growth.

Front

What is the formula for exponential growth?

Back

The formula is P(t) = P0 * e^(rt), where P0 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 N(t) = N0 * e^(-kt), where N0 is the initial amount, k is the decay constant, and t is time.

Front

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

Back

The constant 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth and decay models.