Alg 1 Final Review #3

Front

What is a recursive formula?

Back

A recursive formula defines the terms of a sequence using previous terms. It typically includes an initial term and a rule for finding subsequent terms.

Front

Given the sequence 15, 12, 9, 6, 3, what is the recursive formula?

Back

a_1 = 15, a_n = a_{n-1} - 3.

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 the base, and x is the exponent.

Front

How do you find the equation of an exponential function from a table?

Back

Identify the initial value (a) and the growth factor (b) by examining the ratios of consecutive outputs.

Front

Given the population of algae starts at 500 and triples every hour, what is the function representing this growth?

Back

y = 500(3)^x.

Front

What is the difference between a linear function and an exponential function?

Back

A linear function has a constant rate of change, while an exponential function has a variable rate of change that increases or decreases multiplicatively.

Front

What does the term 'initial value' refer to in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the function f(x) = a * b^x.

Front

What is the general form of a recursive formula for an arithmetic sequence?

Back

a_n = a_{n-1} + d, where d is the common difference.

Front

What is the common difference in the sequence 15, 12, 9, 6, 3?

Back

The common difference is -3.

Front

What is the general form of a recursive formula for a geometric sequence?

Back

a_n = a_{n-1} * r, where r is the common ratio.