Question

WILL GIVE BRAINLIEST Patrick decided to start his own business. his business made 35,000 the first year his profits have increased annually by an average of 2.5%

a. write and iterative (explicit) rule to model the sequence formed by patricks profits each year. Show your work

b. use the rule you wrote to determine what the profits will be after twelve years from the start of his business. round your answer to the nearest dollar. do not round until the end! show all fo your work

Answer 1

(a)

his profits increase annually by 2.5%, thus the profits each year form a geometric sequence with r = 1.025

that is 100 + 2.5 = 102.5% = 1.025

$a_{n}$ = 35000 × $(1.025)^{n-1}$ ← explicit rule

(b)

$a_{12}$ = 35000 × $(1.025)^{11}$ = 45923....

Profits after 12 years ≈ $46000