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 describes growth or decay processes.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function f(x) = a(b)^x is typically y = 0, meaning the graph approaches the x-axis but never touches it.

Front

How do you determine if a function is exponential growth or decay?

Back

If the base b in f(x) = a(b)^x is greater than 1, the function represents exponential growth. If 0 < b < 1, it represents exponential decay.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a(b)^x is the value of f(0), which equals a. This is the point where the graph crosses the y-axis.

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers, represented as (-∞, ∞).

Front

What is the range of an exponential growth function?

Back

The range of an exponential growth function is (0, ∞), meaning it can take any positive value but never reaches zero.

Front

What is the range of an exponential decay function?

Back

The range of an exponential decay function is (0, a), where a is the initial value, meaning it approaches zero but never reaches it.

Front

How do you model exponential decay?

Back

Exponential decay can be modeled with the function f(t) = a(1 - r)^t, where a is the initial amount, r is the decay rate, and t is time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is f(t) = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

Front

What does the term 'asymptote' mean in relation to exponential functions?

Back

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is usually y = 0.