Question

A private museum charges $40 for a group of 10 or fewer people. A group consisting of more than 10 people must, in

addition to the $40, pay $2 per person for the number of people above 10. For example, a group of 12 pays $44. The
maximum group size is 50.
a) How much does a group of 16 pay?
b) Find a formula for the cost function.
c) What are the domain and range of the cost function? (Hint: Use the graph on the calculator)

Answer 1

i hope this helpes

Explanation:

a) A group of 16 pays $40 + ($2 x (16 - 10)) = $40 + $6 = $46.

b) The cost function can be represented as C(x) = 40 + 2(x - 10) for x > 10 and C(x) = 40 for x <= 10, where x is the number of people in the group and C(x) is the cost for the group.

c) The domain of the cost function is all non-negative real numbers less than or equal to 50 (0 <= x <= 50), since the maximum group size is 50. The range of the cost function is all non-negative real numbers greater than or equal to 40 (C(x) >= 40), since the minimum charge for a group is $40.

Answer 2

a) $52

b) C(x) = 40 + 2x, if x > 10 and x ≤ 50

C(x) = 40, if x ≤ 10

c) Domain = {x ≥ 1 and x ≤ 50}

Range = { from 40 to 140}