Question

Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers throughout the season. Each year, he has increased his fee by the same amount. The table shows what Elliot charged each customer for two given years of his business:
year Lawn Care Fee
2000 $750
2010 $1350

A. What is the rate of change and initial value for Elliot’s business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Elliot charges each year.

Answer 1

He started the business in 2000.
In 2000 he charged $750.
What is the initial value?

Answer 2

tbh i really don't know (sorry for being dumb lol)

Answer 3

wait

Answer 4

Do you know what the word "initial" means?

Answer 5

yeah its when you have something at the very beginning

Answer 6

btw thnx for responding

Answer 7

Correct.
He began his lawn service in 2000.
The original amount he charged, the initial amount, was $750.
The amount he charges started at $750 and increases each year.
Part of Part A is what is the initial amount he charged? In other words, what did he charge at the very beginning?

Answer 8

You're welcome.

Answer 9

tysm youre the best

Answer 10

like it nobody was gonna answer my question and u were the only one

Answer 11

Thanks, but let's get back to the problem.
What was the initial amount he charged?

Answer 12

ok he started at $750 so was the initial amount 750??

Answer 13

A. What is the rate of change ----> We'll answer this soon
and initial value for Elliot’s business? ----> The initial value is $750

Answer 14

Correct.
Now let's look at the other part of Part A.
We are looking for the rate of change.

Answer 15

A rate of change is a ratio of the amount of change to the time it took for the change to occur.

Answer 16

mhmm mhmm

Answer 17

We were told he started charging $750 in the year 2000.
We are also told he charged $1350 in the year 2010.

He did not charge $750 per year every year from 2000 to 2009, and then all of a sudden he raised his charge to $1350 for 2010.
We are told he raised the same amount each year.
In 2000 he charged $750.
In 2001 it wen up a certain amount.
In 20002, it wen up by the same amount.
etc.
By the time 2010 came along, the charge was $1350.

Answer 18

The rate of change is the amount he raised his fee by each year.
We can calculate it.
If he charged $750 in 2000 and $1350 in 2010, how much more did he charge in 2010 than in 2000?

Answer 19

"If he charged $750 in 2000 and $1350 in 2010, how much did he charge in 2010 than in 2000?" Wouldn't that be $1350?

Answer 20

No.
He did not start by charging 0.
He started by charging $750.
His fee went up from $750 to $1350.
$1350 is how much more than $750?
What is the difference between $1350 and $750?

Answer 21

Jesus, I am an idiot, I have no idea what the difference is other than the amount increasing. I am so sorry you have to put up with me.

Answer 22

First of all, you're not an idiot.
If you were, you wouldn't bother asking questions.
Just the fact that you don't understand something yet does not make you an idiot.
Soon, you'll understand this, and you'll see how smart you are.

Answer 23

Ah, stop it, you! :^D

Answer 24

The word "difference" in math refers to a subtraction.

Here is an example:
What is the difference between 8 and 5?
8 - 5 = 3.
The difference between 8 and 5 is 3.

Ok? Difference means subtraction.

Answer 25

Now we need the difference between $1350 and $750.
Difference means subtraction, so subtract $1350 - $750

Answer 26

omg how did i not know that

Answer 27

ok its 600

Answer 28

Great.
The amount of change in his fee over 10 years is $600.
His fee went up from $750 to $1350 over a period of 10 years.
Each of those 10 years, the fee went up by the same amount.
To find how much it went up each year, we divide $600 by 10.
That will give us the rate of change.

Answer 29

What is the rate of change?
What is $600/10 ?

Answer 30

60

Answer 31

?

Answer 32

Correct.
Now let's see if we are correct.
I'll construct a table.

Answer 33

kk