Exponential Growth or 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 goes on.

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 time goes on.

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 house is worth $200,000 and appreciates at 3% per year, what is its value after 1 year?

Back

Value after 1 year = 200,000 * (1 + 0.03) = $206,000.

Front

If a car is worth $25,000 and depreciates at 20% per year, what is its value after 1 year?

Back

Value after 1 year = 25,000 * (1 - 0.20) = $20,000.

Front

What does a positive growth rate indicate?

Back

A positive growth rate indicates that the quantity is increasing over time.

Front

What does a negative growth rate indicate?

Back

A negative growth rate indicates that the quantity is decreasing over time.

Front

How does population growth relate to exponential growth?

Back

Population growth can often be modeled as exponential growth when the population increases at a constant percentage rate.

Front

How does population decline relate to exponential decay?

Back

Population decline can often be modeled as exponential decay when the population decreases at a constant percentage rate.