Author:
Hannah Hynes-Petty
Subject:
Mathematics
Material Type:
Assessment, Homework/Assignment, Lesson
Level:
High School
Tags:
  • Exponential
  • Washington Office of Superintendent of Public Instruction
  • wa-math
  • washington-office-of-superintendent-of-public-inst
  • License:
    Creative Commons Attribution Non-Commercial Share Alike
    Language:
    English
    Media Formats:
    Downloadable docs

    Education Standards

    OSPI Exponential Instructional Task: Income

    OSPI Exponential Instructional Task: Income

    Overview

    This resource was created by the Washington Office of Superintendent of Public Instruction. 

    Task

    OSPI Exponential Instructional Task F

    Exponentials; F-LE.3, Claim 4F, Claim 3B

    Exponential Income

    After graduating from college, Adara and Isaac take jobs at IT companies. The amount of money each earned in the first three years is listed in the tables below.

    Adara’s Earned Money                                         Isaac’s Earned Money

    Number of Years

    Pay in $

    0

    100,000

    1

    101,000

    2

    101,975

    3

    103,005

    Number of Years

    Pay in $

    0

    20,000

    1

    25,000

    2

    31,200

    3

    39,119

     

    It can be assumed that the rate of payment will continue to be similar for each job.

    • Write a function for Adara’s earned money you could use to model her future earnings.
    • Write a function for Isaac’s earned money you could use to model his future earnings.

    Adara states that she will always earn more money than Isaac no matter how long they stay with these same companies.

    • Provide a counterexample, using numbers and words, to show that her statement is not valid.

    Rubric

    Rubric

    Question Number

    Standard/Claim

    Description

    F

    F-LE.3/Claim 4F

    F-LE.3/ Claim 4F

    F-LE.3/Claim 3A

    A 3-point response demonstrates full and complete understanding of the standard and claims by doing all the following:

    • Writes  where  is in the interval
    • Writes  where  is in the interval
    • [1.248, 1.254].
    • States a specific counterexample by year when Isaac’s pay is higher than Adara’s pay.

     

    A 2-point response demonstrates reasonable understanding of the standard and claims by doing two the following:

    • Writes  where  is in the interval
    • Writes  where  is in the interval
    • [1.248, 1.254].
    • States a specific counterexample by year when Isaac’s pay is higher than Adara’s pay.

     

    A 1-point response demonstrates partial understanding of the standard and claims by doing one of the following:

    • Writes  where  is in the interval
    • Writes  where  is in the interval
    • [1.248, 1.254].
    • States a specific counterexample by year when Isaac’s pay is higher than Adara’s pay.

     

    A 0-point response demonstrates almost no understanding of the standard and claims.

     

     

    Instructional Exemplar

    OSPI Exponential Instructional Exemplar F

    Exponentials; F-LE.3, Claim 4F, Claim 3B

    After graduating from college, Adara and Isaac take jobs at IT companies. The amount of money each earned in the first three years is listed in the tables below.

    Adara’s Earned Money                                         Isaac’s Earned Money

    Number of Years

    Pay in $

    0

    100,000

    1

    101,000

    2

    101,975

    3

    103,005

    Number of Years

    Pay in $

    0

    20,000

    1

    25,000

    2

    31,200

    3

    39,119

     

    It can be assumed that the rate of payment will continue to be similar for each job.

    • Write a function for Adara’s earned money you could use to model her future earnings.
    • Write a function for Isaac’s earned money you could use to model his future earnings.

    Adara states that she will always earn more money than Isaac no matter how long they stay with these same companies.

    • Provide a counterexample, using numbers and words, to show that her statement is not valid.

     

    • Each year Adara’s earns about $1000 more. I could use the function

     where  is the number of years and   is her pay in dollars.

     

    •                                                        

     

    Isaac’s pay goes up exponentially. A function I could use for Isaac’s pay could be

     where  is the number of years and  is his pay in dollars.

     

    • Isaac’s pay is increasing pretty quickly so I tried guess and check beginning with 10 years. Adara would have $110,000 and Isaac would have   That is way more than Adara makes.