7.1 Graph Exponential Functions

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 it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a(b)^x is greater than 1, resulting in the function increasing rapidly as 'x' increases.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b)^x is between 0 and 1, resulting in the function decreasing rapidly as 'x' increases.

Front

Identify the y-intercept of the function f(x) = 5(2)^x.

Back

The y-intercept is 5, which is the value of the function when x = 0.

Front

How do you determine if a function is exponential growth or decay from its equation?

Back

If the base 'b' is greater than 1, it is exponential growth. If the base 'b' is between 0 and 1, it is exponential decay.

Front

What is the y-intercept of the function f(x) = 3(0.5)^x?

Back

The y-intercept is 3.

Front

What is the general form of an exponential function?

Back

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

Front

If f(x) = 4(1.1)^x, is this function exhibiting growth or decay?

Back

This function is exhibiting exponential growth because the base 1.1 is greater than 1.

Front

If f(x) = 7(0.9)^x, is this function exhibiting growth or decay?

Back

This function is exhibiting exponential decay because the base 0.9 is between 0 and 1.

Front

What is the initial value in the function f(x) = 10(3)^x?

Back

The initial value is 10.