Parts of Exponential Functions - 11/29/23

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 'a' represent in the exponential function f(x) = a(b^x)?

Back

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

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in the function's value as x increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in the function's value as x increases.

Front

In the function f(x) = 90(1/2)^x, what type of exponential behavior does it exhibit?

Back

It exhibits exponential decay because the base (1/2) is less than 1.

Front

What is the growth rate in the function f(x) = 3(2^x)?

Back

The growth rate is 2, meaning the quantity doubles for each unit increase in x.

Front

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

Back

To determine the y-intercept, evaluate the function at x = 0. For f(x) = a(b^x), the y-intercept is 'a'.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(b^x), where 0 < b < 1.

Front

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

Back

The base 'b' indicates the growth or decay factor. If b > 1, the function represents growth; if 0 < b < 1, it represents decay.

Front

In the function f(x) = 300(1.16)^x, what is the initial term?

Back

The initial term is 300, which is the value of the function when x = 0.

Front

What is the significance of the exponent 'x' in an exponential function?

Back

The exponent 'x' represents the independent variable and determines how many times the base is multiplied by itself.