Unit Test- Exponential Functions and Sequences

Front

Fill in the blank: Geometric sequences are graphed as _____________ functions.

Back

Exponential

Front

What is the common ratio of the geometric sequence {2, 10, 50, 250, ...}?

Back

5

Front

Given the recursive formula a_n = a_{n-1} + 5 and a_1 = -16, find the first four terms.

Back

-16, -11, -6, -1

Front

If you have $10 in your bank account and it doubles every month, how much will you have after 5 months?

Back

$320

Front

Mark took a loan for $25,690 at an interest rate of 5.2% compounded monthly. How much will he have paid after 5 years?

Back

$33,299.42

Front

Define a geometric sequence.

Back

A sequence 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 formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

Explain the difference between linear and exponential growth.

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Front

What is the common ratio in the sequence 3, 9, 27, 81?

Back

3