CCF - Compare and Contrast Rates of Change (Lesson)
Compare and Contrast Rates of Change
In this lesson, we will focus on Linear and Exponential Functions.
Salary Practice
Let's compare two situations.
You are deciding between two jobs, both pay $1000 a month. With Job A you get a $100 a month raise, and with Job B you get an 8% raise each month. Which job should you take?
Start by completing the table below:
|
Monthly Salary |
||
|
Month |
$100 raise per month |
8% raise per month |
|
0 |
$1000 |
$1000 |
|
1 |
$1100 |
Solution |
|
2 |
$1200 |
$1166.40 |
|
3 |
$1300 |
$1259.71 |
|
4 |
$1400 |
Solution |
|
5 |
$1500 |
$1469.32 |
|
6 |
$1600 |
$1586.87 |
|
7 |
$1700 |
Solution |
|
8 |
$1800 |
$1850.93 |
|
9 |
$1900 |
$1999.00 |
|
10 |
$2000 |
Solution |
Answer the following questions about the different job options:
- Does Job A grow by a constant rate or a constant percent? Give the constant rate or constant percent change.
- Does Job B grow by a constant rate or a constant percent? Give the constant rate or percent change.
- How many months does it take for Job B to surpass the salary of Job A?
- Do you think Job A will ever catch up in salary to Job B?
Tell whether each quantity is changing by a constant rate per unit of time or constant percent rate per unit of time, or neither.
- Amy's salary is $40,000 in her first year on the job with a $2,000 raise each year thereafter.
- Carla's salary is $50,000 plus a 1% commission on all sales.
- Enrollment at a school is 976 initially and it declines by 2.5% each year.
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
It is important that you can not only identify what type of function you are working with, but also be able to write a function to represent a situation. Watch this video to practice:
Write a Function Practice
Write a function to represent the following situations.
- Ted has $40 in the bank and he plans on adding $5 each week. Write a function, S, representing how much Ted has saved after x weeks.
- Nate has $40 in the bank and plans on increasing his savings by 5% each week. Write a function, S, representing how much Nate has saved after x weeks.
- Julie has $40 in the bank and plans on saving $10 each week. Write a function S, representing how much Julie has saved after x weeks.
- Laura has $40 in the bank and plans on increasing her savings by 7% each week. Write a function, S, representing how much Laura has saved after x weeks.
TO VIEW THE SOLUTIONS ONCE YOU HAVE PRACTICED, CLICK HERE. Links to an external site.
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