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 is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of 'a', which represents the initial value when x = 0.

Front

How do you find the y-intercept of f(x) = 13(0.27)^x?

Back

To find the y-intercept, substitute x = 0: f(0) = 13(0.27)^0 = 13.

Front

What is the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the function's value changes as x increases by 1.

Front

If f(x) = 3^x, what is the y-intercept?

Back

The y-intercept is 1, since f(0) = 3^0 = 1.

Front

What does the expression 10x^-2 simplify to?

Back

10x^-2 simplifies to 10/(x^2).

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases multiplicatively.

Front

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

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.

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 base of an exponential function?

Back

The base of an exponential function is the constant 'b' in the function f(x) = a * b^x, which determines the growth or decay rate.