Question

A new fitness center opened up with 24 clients. Each week they are signing up an average of 5 new members. The business owner wrote the explicit formula for this situation as being A(n) = 24 + (n - 1)(5). Is this correct for this situation? Justify your answer using complete sentences and proper grammar.

Answer 1

@freckles

Answer 2

so i think no .. They start with 24. And get 5 a week. I am assuming the n stands for the week.
A=24 + 5(n)  am i right ?

Answer 3

it depends on what we count as week 1. Normally people count week 1 as the starting point (where A = 24)
so you would want the formula in the question
A= 24 + (n-1)*5

Answer 4

Your equation
A(n)= 24+5n
means you start counting at n=0
we could do that, but (unfortunately) the people who wrote this question assume we start at n=1. They assume that, because that is how sequences are often taught, and they don't expect the student to think too much about it.

Answer 5

but why would n -1 ?

Answer 6

you want A(1) to be 24
if you use A(n)= 24+5*n
we would get A(1)= 24+5*1 = 29 (i.e. 5 too many)
to fix it up, we first subtract 1 from n. now it will work
A(1)= 24
A(2)= 29 (5 more)
A(3)= 34 , etc

Answer 7

Ohhhhh , thank you !

Answer 8

The formula tells you how to figure out how many members there will be, depending on the week. We start with week 1 , with 24 members