Mathematics

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?

1 Answer

  • Answer:

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

    In other words Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]

    Step-by-step explanation:

    [tex]C(x)=80-4x[/tex]

    Let after [tex]t[/tex] weeks she has left no money.

    [tex]c(t)=0\\80-4t=0\\4t=80\\t=20[/tex]

    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 [tex]x[/tex] can be any number between [tex]1[/tex] and [tex]20[/tex]

    Hence Domain[tex]=\{x|x\ is\ an\ integer\ and\ 1\leq x\leq20\}[/tex]

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