Exponential Growth and Decay

Front

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. Example: Population growth where the number doubles at regular intervals.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, leading to a rapid decline. Example: Radioactive decay of a substance.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph shows a rapid increase or decrease, forming a curve that is not a straight line. It typically has a horizontal asymptote.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = 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 does the base 'b' represent in an exponential function?

Back

The base 'b' represents the growth or decay factor. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

What is a common real-world example of exponential growth?

Back

A common example is compound interest in finance, where the amount of interest earned grows exponentially over time.

Front

What is a common real-world example of exponential decay?

Back

A common example is the decay of radioactive materials, where the amount of substance decreases exponentially over time.

Front

How do you calculate the half-life in exponential decay?

Back

The half-life is the time required for a quantity to reduce to half its initial value. It can be calculated using the formula: t(1/2) = ln(2) / k, where k is the decay constant.

Front

What is the significance of the y-intercept in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0. It indicates the starting point of growth or decay.