Exponential Growth and Decay Warm Up

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the base of an exponential function determine?

Back

The base determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential 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 a function of the form f(x) = a(b)^x where b > 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, represented by a function of the form f(x) = a(b)^x where 0 < b < 1.

Front

Identify the function that represents exponential growth: y = 3(2)^x or y = 5(0.5)^x.

Back

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

Front

Identify the function that represents exponential decay: y = 4(3)^x or y = 2(0.25)^x.

Back

y = 2(0.25)^x represents exponential decay.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b)^x, where a > 0 and b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b)^x, where a > 0 and 0 < b < 1.

Front

How can you tell if a function is exponential by looking at its graph?

Back

An exponential function's graph will show a rapid increase (growth) or decrease (decay) and will not form a straight line.

Front

What is the value of the base in the function f(x) = 5(3)^x?

Back

The base is 3.