Unit 1: Modeling Unit Functions

1

Arithmetic Sequences

Note, if a series is arithmetic, the entire series must have a common difference.
Therefore, if one item in the series is not common, then the series is not arithmetic.

1. Complete the table of values for the function 𝑓 𝑥 = 2𝑥 + 5 and the sequence 𝑎𝑛 = 2(𝑛 − 1) + 7. What do you notice?

2. Graph the function 𝑓 𝑥 = 2𝑥 + 5 and the sequence 𝑎𝑛 = 2(𝑛 − 1) + 7. What do you notice?

Real World Examples of Arithmetic
Sequences 𝑦 = 𝑚𝑥 + 𝑏 where m is the
slope or change and b is the constant.

• Go to uhaul.com and see if you can discover the arithmetic

sequence for renting a truck. What is the Explicit formula for
renting a small truck at Uhaul? You can also go to Home
Depot or Lowes to run a truck or tool. Can you model the
rental fee at one of those stores?

• Cobb County host the county fair at Jim Miller Park. You must

pay an entrance fee plus a fee to ride. Can you model this
scenario using an arithmetic sequence? If so, what is the
explicit formula that models this scenario?

When a word problem involves a constant rate or speed and a beginning amount, it can be written in slope-intercept
form: y = mx + b. To do this, recognize which number will represent m, the rate, and which number will represent b,
the y-intercept.

1. An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane

continues at the same rate of descent. The plane’s height and minutes above the ground are related to each other.
Identify the variables in this situation: x = ____________ y = ___________.
a. What is the given information in this problem (find all that apply)? y-intercept ________ slope _____
b. Write an equation to model the situation. b. Use your equation to find the altitude of the plane after 5

minutes.

c.What is the domain and range of the model?

2. Suppose you receive $100 for a graduation present, and you deposit it in a savings account. Then each week

thereafter, you add $5 to the account but no interest is earned. The amount in the account is a function of the
number of weeks that have passed. Identify the variables in this situation: x = ________ y = ______________
a. What is the given information in this problem (find all that apply)? y-intercept ________ slope _____ a. Find

an equation for the amount y you have after x weeks.

b. Use your equation to find when you will have $310 in the account.
c.What is the domain and range of the model?

Word Problems in Slope-intercept Form

Rational vs Irrational