Question

Taylor buys nail polish from a shop that cost $3.95 each. She has a maximum of $30 to spend on nail polish purchases. The total cost, with respect to polishes purchased, can be modeled by a function. Which statement correctly defines the domain of the function?

Answer 1

Answer:

$C_t=3.95x,\ 0\leq x\leq 7$

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

$C_t=3.95x$

But we know Taylor has a limited budget of $30, so the total cost cannot exceed that amount

$3.95x\leq 30$

Solving the inequality for x

$x\leq 30/3.95$

$x\leq 7.6$

We round down to

$x\leq 7$

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

$\boxed{C_t=3.95x,\ 0\leq x\leq 7}$