12/03 - CTG: Exponential Functions Review

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 a positive real number, and 'x' is the exponent.

Front

What does the horizontal asymptote of an exponential function represent?

Back

The horizontal asymptote of an exponential function represents the value that the function approaches as x approaches positive or negative infinity.

Front

What is the initial value in the function f(x) = a(b)^x?

Back

The initial value is the value of the function when x = 0, which is equal to 'a'.

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a constant percentage over equal intervals of time, represented by a function where the base 'b' is greater than 1.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a constant percentage over equal intervals of time, represented by a function where the base 'b' is between 0 and 1.

Front

How do you identify exponential growth from a table of values?

Back

Exponential growth can be identified if the values in the table increase by a constant percentage rate.

Front

How do you identify exponential decay from a table of values?

Back

Exponential decay can be identified if the values in the table decrease by a constant percentage rate.

Front

What is the horizontal asymptote for the function f(x) = 2(3)^x?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote for the function f(x) = 13(0.5)^x?

Back

The horizontal asymptote is y = 0.

Front

What does it mean if a function is growing by a constant rate?

Back

If a function is growing by a constant rate, it is linear, not exponential.