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. It represents growth or decay processes.

Front

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

Back

The 'a' represents the y-intercept or initial value of the function, indicating the value of f(x) when x = 0.

Front

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

Back

The 'b' represents the base of the exponential function, which determines the rate of growth (if b > 1) or decay (if 0 < b < 1).

Front

How do you identify an exponential function from a table of values?

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by the same amount.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a(b^x) where b > 1.

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 is the slope in the linear equation y = mx + b?

Back

In the linear equation, 'm' represents the slope, which indicates the rate of change of y with respect to x.

Front

How do you convert a linear equation to an exponential form?

Back

To convert a linear equation to an exponential form, identify the initial value and the growth factor, then express it as f(x) = a(b^x).

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.

Front

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

Back

The y-intercept is the value of f(x) when x = 0, which is f(0) = 3(2^0) = 3.