Exponential Growth/Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase. For example, if a population doubles every year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay is the process where a quantity decreases by a consistent percentage over time. For example, radioactive substances decay at a rate proportional to their current amount.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a(b)^x, where 'a' is a constant, 'b' is the base (b > 0), and 'x' is the exponent.

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' in an exponential function determines the rate of growth or decay. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

How do you find the y-intercept of an exponential function?

Back

To find the y-intercept of an exponential function, substitute x = 0 into the equation. The y-intercept is the value of y when x is 0.

Front

What is the y-intercept of the function y = 2(3)^x?

Back

The y-intercept is 2, since when x = 0, y = 2(3)^0 = 2.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount. Exponential growth accelerates over time, while linear growth is steady.

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What is a real-world example of exponential growth?

Back

A real-world example of exponential growth is the spread of a virus, where each infected person can infect multiple others, leading to a rapid increase in cases.

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What is a real-world example of exponential decay?

Back

A real-world example of exponential decay is the depreciation of a car's value over time, where the value decreases by a percentage each year.

Front

How can you identify exponential growth from a graph?

Back

Exponential growth can be identified on a graph by a curve that rises steeply as x increases, indicating that the y-values increase rapidly.