Question

Lexi has $80 to spend on an ice cream treat each week. If she spends $4 on ice cream per week, the function C(x)=80−4x

C
(
x
)
=
80
-
4
x
represents how much ice cream money, C, Lexi has left after a certain number of weeks, x. What is the domain in the context of the problem? Why?

Answer 1

Domain
`=\{1,2,3,4,5,6,7,8,9,10,11,12,,13,14,15,16,17,18,19,20\}`

In other words Domain
`=\x`

Explanation:

`C(x)=80-4x`

Let after
`t` weeks she has left no money.

`c(t)=0\\80-4t=0\\4t=80\\t=20`

That means she can have money for ice cream from the week 1 to week 20 and after that she will have no money.

So
`x` can be any number between
`1` and
`20`

Hence Domain
`=\x\ is\ an\ integer\ and\ 1\leq x\leq20\`