Exponential Growth and 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. Example: Population growth.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. Example: Radioactive decay.

Front

What is the general form of an exponential function?

Back

The general form is y = a * b^x, where 'a' is the initial value, 'b' is the growth (b > 1) or decay (0 < b < 1) factor, and 'x' is the exponent.

Front

What is an asymptote in the context of exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often y = 0.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of the function y = a * b^x?

Back

The range is (0, ∞) if a > 0, and (-∞, 0) if a < 0.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth graphs rise sharply and curve upwards, indicating that the rate of increase accelerates over time.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay graphs fall sharply and curve downwards, indicating that the rate of decrease slows over time.

Front

What is the effect of changing the base 'b' in an exponential function?

Back

Changing the base 'b' affects the rate of growth or decay. A larger base results in faster growth, while a base between 0 and 1 results in faster decay.

Front

What is the y-intercept of the function y = a * b^x?

Back

The y-intercept occurs at x = 0, which is y = a.