Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, leading to growth that accelerates over time.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a decrease that slows down over time.

Front

Define the Decay Factor.

Back

The Decay Factor is the multiplier used to calculate the remaining quantity after a decay process, calculated as (1 - decay rate).

Front

If a population decreases by 6% per year, what is the decay factor?

Back

0.94 (1 - 0.06 = 0.94).

Front

How do you calculate the population after a certain number of years with exponential decay?

Back

Use the formula: P = P0 * (decay factor)^t, where P0 is the initial population, and t is the number of years.

Front

What is the formula for Exponential Growth?

Back

The formula is: P = P0 * (1 + r)^t, where P0 is the initial amount, r is the growth rate, and t is time.

Front

What is the difference between Linear Growth and Exponential Growth?

Back

Linear Growth increases by a constant amount, while Exponential Growth increases by a constant percentage, leading to faster growth over time.

Front

If a car depreciates from $20,000 to $15,000 in one year, what is the decay factor?

Back

0.75 (15,000 / 20,000 = 0.75).

Front

What is the future value of an investment with compound interest?

Back

Future Value = Principal * (1 + interest rate)^number of periods.

Front

Calculate the future value of $600 invested at 5% interest for 5 years.

Back

$765.77.