Attributes of 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 a positive real number, and 'x' is the exponent.

Front

What is the general form of an exponential growth function?

Back

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

Front

What is the general form of an exponential decay function?

Back

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

Front

What does the base 'b' represent in an exponential function?

Back

The base 'b' determines the rate of growth or decay; if b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

How do you find the y-intercept of an exponential function?

Back

The y-intercept can be found by evaluating f(0), which gives the value of 'a' in the function f(x) = a(b)^x.

Front

What is the y-intercept of the function f(x) = 3(2)^x?

Back

The y-intercept is (0, 3).

Front

What is the y-intercept of the function f(x) = 5(0.5)^x?

Back

The y-intercept is (0, 5).

Front

What type of function is f(x) = 4(1/3)^x?

Back

Exponential Decay.

Front

What type of function is f(x) = 7(3)^x?

Back

Exponential Growth.

Front

What is the effect of increasing the value of 'a' in an exponential function?

Back

Increasing 'a' results in a vertical stretch of the graph, making it grow faster.