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(b)^x, where b > 1.

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(b)^x, where 0 < b < 1.

Front

Identify the growth or decay in the equation: y = 5(2)^x.

Back

Exponential growth (b = 2 > 1).

Front

Identify the growth or decay in the equation: y = 3(0.5)^x.

Back

Exponential decay (b = 0.5 < 1).

Front

Which of the following represents exponential growth: y = 4(3)^x or y = 4(0.3)^x?

Back

y = 4(3)^x represents exponential growth.

Front

Which of the following represents exponential decay: y = 10(1.1)^t or y = 10(0.9)^t?

Back

y = 10(0.9)^t represents exponential decay.

Front

What does the base 'b' represent in the exponential function y = a(b)^x?

Back

The base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor.

Front

If a population doubles every year, what type of growth is this?

Back

Exponential growth.

Front

If a substance decreases to half its amount every year, what type of decay is this?

Back

Exponential decay.

Front

What is the general form of an exponential function?

Back

y = a(b)^x, where 'a' is the initial value and 'b' is the growth/decay factor.