Exponential Growth & 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

How do you calculate the future value in Exponential Growth?

Back

Future Value = Present Value × (1 + growth rate)^number of periods.

Front

How do you calculate the future value in Exponential Decay?

Back

Future Value = Present Value × (1 - decay rate)^number of periods.

Front

What is the formula for Exponential Growth?

Back

y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for Exponential Decay?

Back

y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If a population of 100 increases by 20% each year, what will it be after 3 years?

Back

Future Population = 100 × (1 + 0.20)^3 = 182.43 (approximately 182).

Front

If a car's value is $20,000 and it depreciates by 15% each year, what will its value be after 2 years?

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Future Value = 20000 × (1 - 0.15)^2 = 14,450 (approximately).

Front

What is a common application of Exponential Growth in real life?

Back

Population growth, compound interest in finance, and viral spread of diseases.

Front

What is a common application of Exponential Decay in real life?

Back

Radioactive decay, depreciation of assets, and cooling of hot objects.