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.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: its the third option.

step-by-step explanation:

i just took the test.