Question

(1 point)
the copy shoppe charges 0.1 dollars per copy for quantites up to and included 108 copies. for quantities above 108, the charge is 0.08 dollars per copy plus an unknown constant k. if x represents the number of copies, the price function is:
p(x)=\

$$\begin{cases}0.1x&x \\leq 108 \\\\ 0.08x + k&x>108\\end{cases}$$

find the value of k that makes the price function continuous for all values of x.
the price function is continuous if k =
round to three decimal places if needed.

Explanation:

Step1: Recall continuity condition

For a function to be continuous at $x = 108$, $\lim_{x
ightarrow108^{-}}p(x)=\lim_{x
ightarrow108^{+}}p(x)$.

Step2: Calculate left - hand limit

$\lim_{x
ightarrow108^{-}}p(x)=0.1\times108 = 10.8$.

Step3: Calculate right - hand limit

$\lim_{x
ightarrow108^{+}}p(x)=0.08\times108 + k=8.64 + k$.

Step4: Set left and right limits equal

Set $10.8=8.64 + k$.

Step5: Solve for k

$k=10.8 - 8.64=2.16$.

Answer:

$2.160$