- Author:
- Hannah Hynes-Petty
- Subject:
- Mathematics
- Material Type:
- Assessment, Homework/Assignment, Lesson
- Level:
- High School
- Tags:
- License:
- Creative Commons Attribution Non-Commercial Share Alike
- Language:
- English
- Media Formats:
- Downloadable docs
Education Standards
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:
|
A 2-point response demonstrates reasonable understanding of the standard and claims by doing two the following:
| ||
A 1-point response demonstrates partial understanding of the standard and claims by doing one of the following:
| ||
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.