Unit 1 Lesson 9

A party will have hexagonal tables placed together with space for one person on each open side. List the number of people who can sit if there are 1, 2, 3, 4, and 5 tables.

A party will have hexagonal tables placed together with space for one person on each open side. Describe how the number of people who can sit at the table changes with each step.

• The number of people who can sit at the tables decreases by 4 each time a table is added.

• The number of people who can sit at the tables increases by 6 each time a table is added.

• The number of people who can sit at the tables increases by 5 each time a table is added.

• The number of people who can sit at the tables increases by 4 each time a table is added.

A party will have hexagonal tables placed together with space for one person on each open side. Explain why  $P\left(3.2\right)$  does not make sense in this scenario.

Which recursive definition works for  $P$  and the  $nth$  term? Hint: there are two correct answers here.

•  $P\left(1\right)=6,\ P\left(n\right)=P\left(n-1\right)+4;\ n\ge2$  

•  $P\left(1\right)=6,\ P\left(n\right)=P\left(n-1\right)+5;\ n\ge2$  

•  $P\left(n\right)=4\cdot P\left(n-1\right)+6;\ n\ge1$  

•  $P\left(n\right)=4\cdot P\left(n-1\right)+5;\ n\ge1$  

Diego is making a stack of pennies. He starts with 5 and then adds them 1 at a time. A penny is 1.52 mm thick. Complete the table with the height of the stack  $h\left(n\right),$  in mm, after  $n$  pennies have been added.

A piece of paper has an area of 80 square inches. A person cuts off  $\frac{1}{4}$  of the piece of paper. Then a second person cuts off  $\frac{1}{4}$  of the remaining paper. A third person cuts off  $\frac{1}{4}$  of what is left, and so on. Complete the table where  $A\left(n\right)$  is the area, in square inches, of the remaining paper after the  $nth$  person cuts off their fraction.

A piece of paper has an area of 80 square inches. A person cuts off  $\frac{1}{4}$  of the piece of paper. Then a second person cuts off  $\frac{1}{4}$  of the remaining paper. A third person cuts off  $\frac{1}{4}$  of what is left, and so on. Which equation defines  $A$  for the  $nth$   term?

•  $A\left(n\right)=80\cdot\left(\frac{1}{4}\right)^n;\ n\ge0$  

•  $A\left(n\right)=80\cdot\left(\frac{3}{4}\right)^n;\ n\ge0$  

•  $A\left(n\right)=80\div\left(\frac{3}{4}\right)^n;\ n\ge0$  

•  $A\left(n\right)=80\div\left(\frac{1}{4}\right)^n;\ n\ge0$  

 $\frac{1}{4}$  A piece of paper has an area of 80 square inches. A person cuts off   $\frac{1}{4}$  of the piece of paper. Then a second person cuts off  $\frac{1}{4}$   of the remaining paper. A third person cuts off  $\frac{1}{4}$  of what is left, and so on. What is a reasonable domain for the function  $A?$  REMINDER: domain refers to x-values on a graph.

•  $n\le0,$  because the domain is the number of cuts.

•  $n\ge0$  because the domain is the number of cuts and the paper can be continuously cut.

•  $0\le n\le15$  , since after 15 cuts, there is only about one square inch left. 

Here is the recursive definition of a sequence: $f\left(1\right)=35,\ f\left(n\right)=f\left(n-1\right)-8;\ n\ge2$  List the first 5 terms of the sequence.

Here is a graph of a sequence $q$ Define  $q$  recursively using function notation. 

•  $f(1)=-3,\ f(n)=f(n−1)\cdot3;\ n≥2$  

•  $f(1)=-3,\ f(n)=f(n−1)\cdot\frac{1}{3};\ n≥2$  

•  $f(1)=-3,\ f(n)=f(n−1)-3;\ n≥2$  

•  $f(1)=-3,\ f(n)=f(n−1)+3;\ n≥2$