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

Back

The 'a' represents the y-intercept or initial value of the function.

Front

Identify the y-intercept in the function f(x) = 13 * (0.27)^x.

Back

The y-intercept is 13.

Front

What is the general shape of an exponential growth function?

Back

An exponential growth function increases rapidly as x increases, creating a J-shaped curve.

Front

What is the general shape of an exponential decay function?

Back

An exponential decay function decreases rapidly as x increases, approaching the x-axis but never touching it.

Front

How do 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 type of function does the equation y = 2x + 3 represent?

Back

Linear function.

Front

What is the difference between linear and exponential functions?

Back

Linear functions add or subtract a constant value, while exponential functions multiply or divide by a constant factor.

Front

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

Back

The base 'b' indicates the growth (b > 1) or decay (0 < b < 1) rate of the function.

Front

If f(x) = 5 * (2)^x, what is the value of f(0)?

Back

f(0) = 5 * (2)^0 = 5.