Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to the value increasing rapidly over time.

Front

What is exponential decay?

Back

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

Front

What is the general form of an exponential function?

Back

The general form is f(x) = 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' determines the rate of growth or decay; if b > 1, the function represents growth, and if 0 < b < 1, it represents decay.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote is a line that the graph approaches but never touches, typically y = 0 for exponential functions.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers (-∞, ∞).

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is y > 0.

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is y > 0.

Front

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

Back

The y-intercept is found by evaluating the function at x = 0, which gives f(0) = a.

Front

What is a real-world example of exponential growth?

Back

A common example is population growth, where the population increases rapidly under ideal conditions.