Exponential Growth and Decay Graphing

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates 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 that slows over time.

Front

What does the starting value represent in an exponential function?

Back

The starting value in an exponential function represents the initial amount before any growth or decay occurs.

Front

In the equation y = a(b^x), what does 'a' represent?

Back

'a' represents the initial value or starting amount in the exponential function.

Front

In the equation y = a(b^x), what does 'b' represent?

Back

'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor in the exponential function.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a curve that rises steeply and continuously increases as x increases.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply and continuously decreases as x increases.

Front

What does the equation y = 5000(0.98)^x represent in terms of a bank account?

Back

It represents the amount remaining in a bank account after x years, where 5000 is the initial amount and 0.98 indicates a 2% annual fee.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

What does the term 'inactive account fee' imply in the context of exponential decay?

Back

It implies that the account balance decreases over time due to fees charged for inactivity, modeled by an exponential decay function.