Exponential Growth or 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 as time progresses.

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 as time progresses.

Front

What is the initial value in the function f(x) = 300(1.16)^x?

Back

The initial value is 300.

Front

What does the base in an exponential function represent?

Back

The base represents the factor by which the quantity increases (if greater than 1) or decreases (if between 0 and 1) for each unit increase in x.

Front

Identify the model that represents exponential decay: y = 5(1 + 0.05)^t or y = 5(1 - 0.05)^t?

Back

y = 5(1 - 0.05)^t represents exponential decay.

Front

What is the factor of change in the function f(x) = 300(1.16)^x?

Back

The factor of change is 1.16.

Front

Which of the following is an example of exponential decay: y = 8(1.05)^t or y = 8(0.95)^t?

Back

y = 8(0.95)^t is an example of exponential decay.

Front

What type of graph represents exponential growth?

Back

A graph of exponential growth rises sharply and continuously increases as x increases.

Front

What type of graph represents exponential decay?

Back

A graph of exponential decay falls sharply and continuously decreases as x increases.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(1 + r)^x, where a is the initial value and r is the growth rate.