Exponential Functions Recap

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 it mean for a function to exhibit exponential growth?

Back

A function exhibits exponential growth when the base 'b' in the function f(x) = a * b^x is greater than 1.

Front

What does it mean for a function to exhibit exponential decay?

Back

A function exhibits exponential decay when the base 'b' in the function f(x) = a * b^x is between 0 and 1.

Front

In the function f(x) = a * b^x, what does the variable 'a' represent?

Back

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

Front

In the function f(x) = a * b^x, what does the variable 'b' represent?

Back

The variable 'b' represents the growth (if b > 1) or decay (if 0 < b < 1) factor of the exponential function.

Front

How can you determine if a function is exponential growth or decay from its equation?

Back

You can determine if a function is exponential growth or decay by examining the base 'b': if b > 1, it is growth; if 0 < b < 1, it is decay.

Front

What is the general shape of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises steeply as x increases, starting from the initial value 'a'.

Front

What is the general shape of the graph of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaching the x-axis but never touching it.

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is the x-axis (y = 0), which the graph approaches but never reaches.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.