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. It represents growth or decay at a constant percentage rate.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. For exponential functions, the horizontal asymptote is typically y = 0.

Front

What does the base of an exponential function indicate?

Back

The base of an exponential function indicates the growth or decay factor. 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 initial value in an exponential function?

Back

The initial value in an exponential function is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

Front

How do you identify exponential growth from a graph?

Back

Exponential growth is identified by a graph that rises sharply and increases at an increasing rate as x increases.

Front

How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a graph that falls sharply and decreases at a decreasing rate as x increases.

Front

What does a growth factor of 1.06 represent?

Back

A growth factor of 1.06 represents a 6% growth rate, meaning the quantity increases by 6% each time period.

Front

What does a decay factor of 0.94 represent?

Back

A decay factor of 0.94 represents a 6% decay rate, meaning the quantity decreases by 6% each time period.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.