A museum charges 4 per person for a guided tour wi

Questions: A museum charges 4 per person for a guided tour with a group of 1 to 9 people or a fixed 40 fee for a group of 10 or more people. Write a function relating the number of people, n, to the cost, C. C(n)= if 0<n< if n >=

Transcript text: A museum charges $\$ 4$ per person for a guided tour with a group of 1 to 9 people or a fixed $\$ 40$ fee for a group of 10 or more people. Write a function relating the number of people, $n$, to the cost, $C$. \[ C(n)=\left\{\begin{array}{ll} \square & \text { if } 0

Solution

Solution Steps

To solve this problem, we need to define a function that calculates the cost based on the number of people in a group. If the group size is between 1 and 9, the cost is $4 per person. If the group size is 10 or more, the cost is a fixed $40. We will use a conditional statement to implement this logic.

Step 1: Define the Cost Function

To determine the cost $ C(n) $ based on the number of people $ n $, we need to establish a piecewise function. The cost is calculated differently depending on whether the group size is less than 10 or 10 and above.

Step 2: Calculate Cost for Groups of 1 to 9 People

For a group size $ 1 \leq n < 10 $, the cost is calculated as: \[ C(n) = 4n \] This means each person in the group is charged \$4.

Step 3: Calculate Cost for Groups of 10 or More People

For a group size $ n \geq 10 $, the cost is a fixed amount: \[ C(n) = 40 \] This means the total cost is \$40 regardless of the number of people in the group.