Answer:
[tex]C_t=3.95x,\ 0\leq x\leq 7[/tex]
Step-by-step explanation:
Modeling With Functions
It's a common practice to try to mathematically represent the relation between two or more variables. It allows us to better understand the behavior of the phenomena being observed and, more importantly, to be able to predict future values.
The specific situation stated in the question relates how Taylor buys nail polish for $3.95 each, with a maximum of $30 to spend. If x is the number of nail polish purchased, then the total cost will be
[tex]C_t=3.95x[/tex]
But we know Taylor has a limited budget of $30, so the total cost cannot exceed that amount
[tex]3.95x\leq 30[/tex]
Solving the inequality for x
[tex]x\leq 30/3.95[/tex]
[tex]x\leq 7.6[/tex]
We round down to
[tex]x\leq 7[/tex]
Of course, the lower limit of x is 0, because Taylor cannot purchase negative quantities of nail polish
Our model is now complete if the state the limits of x, or its domain
[tex]\boxed{C_t=3.95x,\ 0\leq x\leq 7}[/tex]
