Unit Test- Exponential Functions and Sequences

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 (a positive real number), and 'x' is the exponent.

Front

How does the value of an exponential function change as 'x' increases?

Back

As 'x' increases, the value of an exponential function increases rapidly if the base 'b' is greater than 1.

Front

What is the formula for compound interest?

Back

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

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

Write the general term for a geometric sequence with first term 'a' and common ratio 'r'.

Back

The general term a_n of a geometric sequence can be expressed as a_n = a * r^(n-1).

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant.

Front

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in an arithmetic sequence.

Front

Write the general term for an arithmetic sequence with first term 'a' and common difference 'd'.

Back

The general term a_n of an arithmetic sequence can be expressed as a_n = a + (n-1)d.

Front

How do you determine if a sequence is arithmetic or geometric?

Back

To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. To determine if it is geometric, check if the ratio of consecutive terms is constant.