Geometric Sequence and Radical Test

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

How do you find the nth term of a geometric sequence?

Back

The nth term can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

Front

What does a decay rate of 10% mean in a geometric sequence?

Back

A decay rate of 10% means that each term is 90% of the previous term, or equivalently, the common ratio is 0.9.

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, r is the decay rate, and x is the time.

Front

What does 1.05 represent in the equation f(x) = 2(1.05)^x?

Back

1.05 represents the rate of growth, indicating that the quantity increases by 5% each time period.

Front

How do you calculate the population after a certain number of years with a decay rate?

Back

To calculate the population after a certain number of years, use the formula: P = P_0 * (1 - r)^t, where P_0 is the initial population, r is the decay rate, and t is the number of years.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What does the inequality y < 2/3x - 3 represent?

Back

The inequality y < 2/3x - 3 represents all the points below the line y = 2/3x - 3 on a graph.

Front

What is the significance of the initial value in an exponential function?

Back

The initial value is the starting point of the function, representing the value of the function when x = 0.