Question

The cost of entry to a museum C depends on the number of people p in a group, according to the piecewise function defined below: C(p)=beginarrayl 5p if 0 9endarray. Find the cost of admission for a group of 8 people and for a group of 12 people.

Answer 1

The cost of admission for a group of 8 people is $40, and for a group of 12 people is $60.

Step-by-step explanation:

The cost of entry to the museum can be found using the piecewise function C(p) = 5p if 0 9:

If the group has 8 people, substitute p = 8 in the function:

C(8) = 5 * 8 = 40

So, the cost of admission for a group of 8 people is $40.

If the group has 12 people, substitute p = 12 in the function:

C(12) = 5 * 12 = 60

So, the cost of admission for a group of 12 people is $60.

Answer 2

For a group of 8 people, the cost of admission would be $40, and for a group of 12 people, it would be $96, based on the piecewise function defining the cost of entry to the museum.

Step-by-step explanation:

The cost of entry to a museum C depends on the number of people p in a group and is defined by a piecewise function. To find the cost of admission for a group of 8 people, we'll use the first part of the function:

C(p) = 5p for p ≤ 9.

For 8 people, the cost would be C(8) = 5 × 8 = $40.

To find the cost of admission for a group of 12 people, we'll use the second part of the function:

C(p) = 8p for p > 9.

For 12 people, the cost would be C(12) = 8 × 12 = $96.