Unit 4 APPC: Exponential Functions and Series

Front

What is the limit of f(x) as x approaches infinity?

Back

The limit of f(x) as x approaches infinity is ∞.

Front

How does the rate of change behave for the graph of an exponential function?

Back

The rate of change is increasing on (-∞, ∞).

Front

What is the formula for the nth partial sum of a geometric series?

Back

The nth partial sum S_n of a geometric series can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where a is the first term and r is the common ratio.

Front

What is the limit of f(x) as x approaches negative infinity?

Back

The limit of f(x) as x approaches negative infinity is 0.

Front

What condition indicates that y = A * B^x is a growth model?

Back

The condition for y = A * B^x to be a growth model is that B > 1.

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 is the common ratio in a geometric series?

Back

The common ratio in a geometric series is the factor by which each term is multiplied to get the next term.

Front

How do you determine the convergence of a geometric series?

Back

A geometric series converges if the absolute value of the common ratio r is less than 1 (|r| < 1).

Front

What is the significance of the base in an exponential function?

Back

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

Front

What is the relationship between exponential functions and their graphs?

Back

The graph of an exponential function is characterized by a rapid increase or decrease, depending on the base, and it approaches the x-axis asymptotically.