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 base in an exponential function represent?

Back

The base in an exponential function determines the growth or decay rate. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

Front

What is the common ratio in the function f(x) = 25(4)^x?

Back

The common ratio is 4.

Front

What is the initial value in the function y = 4(2)^x?

Back

The initial value is 4.

Front

What is the starting amount in the function f(t) = 300(1.05)^t?

Back

The starting amount is 300.

Front

What type of growth does the function f(x) = 2(3)^x represent?

Back

Exponential Growth.

Front

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

Back

The y-intercept is 3.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a graph that decreases rapidly at first and then levels off, approaching the x-axis but never touching it.

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 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 exponentially.