Exponential Growth and Decay

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What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate. It can be modeled by the equation y = a(1 + r)^x, where a is the initial amount, r is the growth rate, and x is time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline. It can be modeled by the equation y = a(1 - r)^x, where a is the initial amount, r is the decay rate, and x is time.

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What does the variable 'y' represent in the equation y = 13000(0.88)^x?

Back

In this equation, 'y' represents the car's value in dollars after 'x' years.

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What does the variable 'x' represent in the equation y = 46000(1.05)^x?

Back

In this equation, 'x' represents the time in years.

Front

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

Back

Use the formula y = a(1 - r)^x, where 'a' is the initial value, 'r' is the rate of depreciation, and 'x' is the number of years.

Front

What is the formula for calculating exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What is the initial value in the equation y = 1450(0.82)^x?

Back

The initial value in this equation is 1450.

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If a car depreciates at a rate of 12% annually, what is the decay factor?

Back

The decay factor is 0.88, calculated as 1 - 0.12.

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What does an exponential function look like on a graph?

Back

An exponential function graph shows a rapid increase (for growth) or decrease (for decay) and is characterized by a curve that becomes steeper over time.

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What is the difference between linear and exponential functions?

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Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.