Exponential Growth/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 the base amount grows.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as the base amount shrinks.

Front

What is the formula for exponential growth?

Back

The formula is A = P(1 + r)^t, where A is the amount after time t, P 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 A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

If a population of 1000 increases by 5% per year, what will it be after 1 year?

Back

A = 1000(1 + 0.05)^1 = 1050.

Front

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

Back

A = 1000(1 - 0.10)^1 = 900.

Front

What does a decay rate of 20% mean?

Back

It means that each year, the quantity decreases by 20% of its current value.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a fixed amount each period, while exponential growth increases by a fixed percentage, leading to larger increases over time.

Front

What is a real-world example of exponential growth?

Back

A common example is population growth, where the number of individuals increases rapidly as the population base grows.

Front

What is a real-world example of exponential decay?

Back

Radioactive decay is a classic example, where the quantity of a radioactive substance decreases over time at a consistent rate.