Question

instructions: round your answers to two decimal places, show your decimal places today. mike is a veterinarian. he is placing a 9 - line job ad for an assistant. the following piecewise function gives the price of an x - line ad.
(a(x)=\begin{cases}45&\text{when }xleq3\\45 + 9(x - 3)&\text{when }x>3end{cases})
(a)) find the difference between the cost of a two - line ad and the cost of a three - line ad.
(b)) find the cost of a 10 - line ad.
(c)) find the cost of an 11 - line ad.

Explanation:

Part a

Step1: Find cost of 2-line ad

For \( x = 2 \), since \( 2\leq3 \), use \( a(x)=45 \). So \( a(2)=45 \).

Step2: Find cost of 3-line ad

For \( x = 3 \), since \( 3\leq3 \), use \( a(x)=45 \). So \( a(3)=45 \).

Step3: Calculate the difference

Difference \( = a(3)-a(2)=45 - 45=0 \).

Step1: Identify the function for \( x = 10 \)

Since \( 10>3 \), use \( a(x)=45 + 9(x - 3) \).

Step2: Substitute \( x = 10 \) into the function

\( a(10)=45+9(10 - 3)=45+9\times7=45 + 63=108 \).

Step1: Identify the function for \( x = 11 \)

Since \( 11>3 \), use \( a(x)=45 + 9(x - 3) \).

Step2: Substitute \( x = 11 \) into the function

\( a(11)=45+9(11 - 3)=45+9\times8=45 + 72=117 \).

Answer:

\( 0 \)

Part b