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For groups of 3030 or more people, a water park charges $18$18 per person for the first 3030 people and $12$12 for each additional person. Which function g𝑔 gives the total charge, in dollars, for a tour group with m𝑚 people, where m≥30𝑚≥30?

Question

For groups of 3030 or more people, a water park charges 181818 per person for the first 3030 people and 121212 for each additional person. Which function g𝑔 gives the total charge, in dollars, for a tour group with m𝑚 people, where m≥30𝑚≥30?

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Solution

The function g(m) that gives the total charge, in dollars, for a tour group with m people, where m≥30, can be defined as follows:

If the group size is exactly 30, the cost is 18perperson.So,thetotalcostis3018 per person. So, the total cost is 30 * 18 = $540.

If the group size is more than 30, the cost is 18perpersonforthefirst30peopleand18 per person for the first 30 people and 12 for each additional person. So, the total cost is 540+540 + 12 * (m - 30).

Therefore, the function g(m) can be defined as:

g(m) = 540 if m = 30 g(m) = 540 + 12 * (m - 30) if m > 30

This problem has been solved

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