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, represented by the function y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' 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 function y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

Identify the growth factor in the function y = 5(1.04)^x.

Back

The growth factor is 1.04.

Front

Identify the decay factor in the function A = 1200(0.85)^6.

Back

The decay factor is 0.85.

Front

What does a growth rate of 4% mean in an exponential growth model?

Back

It means that the quantity increases by 4% of its current value each time period.

Front

What does a decay rate of 15% mean in an exponential decay model?

Back

It means that the quantity decreases by 15% of its current value each time period.

Front

Is the function f(x) = 2(1/7)^x an example of growth or decay?

Back

It is an example of exponential decay.

Front

How can you tell if a function represents growth or decay?

Back

If the base of the exponent is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.

Front

What is the general form of an exponential function?

Back

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

Front

What is the significance of the initial value 'a' in an exponential function?

Back

The initial value 'a' represents the starting amount before any growth or decay occurs.