Exponential Growth and 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 progresses.

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 progresses.

Front

What is the general formula for Exponential Growth?

Back

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 general formula for Exponential Decay?

Back

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 20% each year, what will it be after 1 year?

Back

A = 1000(1 + 0.20)^1 = 1200.

Front

If a car's value is $20,000 and it depreciates by 15% annually, what will its value be after 1 year?

Back

A = 20000(1 - 0.15)^1 = 17000.

Front

What does the term 'half-life' refer to in exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value.

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 n is the number of times interest is compounded per year.

Front

What is the effect of a negative growth rate in exponential functions?

Back

A negative growth rate indicates exponential decay, meaning the quantity decreases over time.

Front

How can you determine if a model represents growth or decay from its equation?

Back

If the base of the exponent is greater than 1, it represents growth; if it is between 0 and 1, it represents decay.