Identify Growth or Decay from Graph/Equation

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, represented by the equation y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, represented by the equation y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

Identify the growth factor in the equation y = 4(1 + 0.08)^t.

Back

The growth factor is 1 + 0.08 = 1.08.

Front

Identify the decay factor in the equation y = 8(1 - 0.5)^x.

Back

The decay factor is 1 - 0.5 = 0.5.

Front

Which equation represents exponential growth: y = 3(2)^x or y = 3(0.5)^x?

Back

y = 3(2)^x represents exponential growth.

Front

Which equation represents exponential decay: y = 5(3)^x or y = 5(0.2)^x?

Back

y = 5(0.2)^x represents exponential decay.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor; if the base is greater than 1, it indicates growth; if the base is between 0 and 1, it indicates decay.

Front

How can you tell if a graph represents exponential growth?

Back

A graph represents exponential growth if it rises sharply and continuously increases without bound as x increases.

Front

How can you tell if a graph represents exponential decay?

Back

A graph represents exponential decay if it falls sharply and approaches zero as x increases.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a(b)^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent.