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 rapid increases as the base amount grows.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed 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

How do you calculate the future value of an investment with compound interest?

Back

Use the formula A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the decay factor in exponential decay?

Back

The decay factor is (1 - r), where r is the decay rate expressed as a decimal.

Front

If a population of bacteria doubles every hour, what type of growth is this?

Back

This is an example of Exponential Growth.

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

How do you determine if a model represents growth or decay?

Back

If the growth rate (r) is positive, it represents growth; if the decay rate (r) is negative, it represents decay.

Front

What is the value of a car that depreciates at 10% per year after 3 years if its initial value was $20,000?

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The value after 3 years is approximately $14,641.00.