Question

1. let ( f(h) ) be the number of customers in a store ( h ) hours after 9 a.m. explain the meaning of each statement.

a. ( f(h) = 38 )
b. ( f(3.5) = f(10) )

in exercises 3–5, solve the inequality. graph the solution.

1. ( 4k - 3 geq 9 )
2. ( 12 - 4q leq 2q + 18 )
3. ( 2(2m + 1) > -2 + 4(1 - m) )

Explanation:

Part 2 (Interpretation of Functions)

a. \( f(h) = 38 \)

The function \( f(h) \) represents the number of customers \( h \) hours after 9 A.M. So \( f(h)=38 \) means that \( h \) hours after 9 A.M., there are 38 customers in the store. Here, \( h \) is a specific number of hours (though not specified in the equation itself, the equation states that at that particular \( h \)-hour mark post 9 A.M., the customer count is 38).

\( f(3.5) \) is the number of customers 3.5 hours after 9 A.M. (which is 12:30 P.M., since \( 9 + 3.5 = 12.5 \) or 12:30 P.M.), and \( f(10) \) is the number of customers 10 hours after 9 A.M. (which is 7 P.M., since \( 9+10 = 19 \) or 7 P.M.). The equation \( f(3.5)=f(10) \) means that the number of customers in the store at 3.5 hours after 9 A.M. (12:30 P.M.) is equal to the number of customers at 10 hours after 9 A.M. (7 P.M.).

Step 1: Add 3 to both sides

To isolate the term with \( k \), we add 3 to both sides of the inequality.
\( 4k - 3 + 3 \geq 9 + 3 \)
Simplifying, we get \( 4k \geq 12 \).

Step 2: Divide by 4

To solve for \( k \), we divide both sides by 4.
\( \frac{4k}{4} \geq \frac{12}{4} \)
Simplifying, we get \( k \geq 3 \).

Answer:

\( h \) hours after 9 A.M., there are 38 customers in the store.

b. \( f(3.5)=f(10) \)