Ahotel chain charges $75 each night for the first two nights and $50 for each additional night’s stay. the total cost t is a function of the number of nights x that a guest stays.

you would need a function to determine whether to use a formula for 1 or 2 nights or a formula for more than 2 nights

T(x)={a if x <_ 2, b if x > 2}

 if it's 2 nights or less use option a, a = 75x

 if its longer than 2 days use option b, b= 50x + 50

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}

Step-by-step explanation:

A hotel chain charges $75 per night for first two nights.

If the number of nights of the stay are x then charges for x nights

= 75x where x ≤ 2

If the stay is for than 2 nights then charges for x nights

= Charges for two first 2 nights(@$75 per night) + charges for other than initial 2 nights (@$50 per night)

= (75×2) + 50x where x > 2

Therefore total cost of the hotel if represented by t then the function will be

t = 75x  {x ≤ 2}

t = 150 + 50x {x > 2}