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.

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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.

Front

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.

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.

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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?

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

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

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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?

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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.

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How can you model population growth using exponential functions?

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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.

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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.