Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay refers to the process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Tags

CCSS.HSF-IF.C.8B

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What is the formula for exponential growth?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The future value can be calculated using the formula FV = P(1 + r/n)^(nt), where P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

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What is depreciation in the context of exponential decay?

Back

Depreciation is the reduction in the value of an asset over time, often calculated using a fixed percentage of the asset's value.

Front

How do you determine the value of an asset after a certain number of years of depreciation?

Back

To determine the value after depreciation, use the formula V = P(1 - r)^t, where P is the initial value, r is the depreciation rate, and t is the number of years.

Front

What is the significance of the base in exponential functions?

Back

The base in exponential functions determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How can you model population growth using exponential functions?

Back

Population growth can be modeled using the formula P(t) = P0e^(rt), where P0 is the initial population, r is the growth rate, and t is time.

Front

What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount over time, while exponential growth increases by a percentage of the current value, leading to faster growth as time progresses.