Answer to Question #299763 in Algebra for Lia

Question

A rental home on EWD apartelle rents for 1,000.00 a night for the first three nights, 900.00 for the next three nights, and 800.00 a night for each remaining night. The total cost T is a function of the number of night's n that a guest stays.

Create a function model defined

Answer 1

Let n be the number of nights a guest stays

we define the following

since first three nights are each 1000, if n≤3, then total cost = 1000n

For the next 3 nights at 900 each, we define total cost as (3*1000) for the first three nights and 900n for 4≤n≤6, thus total becomes 3000 + 900n for 4≤n≤6

For additional nights it is 800 each night, for this case n>6, thus the total cost becomes (3000 + 900n + (n-6)800 ) = (3000 + 900n +800n -4800) = 1700n -1800 for n>6

Thus , we define the function for the total cost T for the number of nights a guest stays as below

T(n) =1000n for n≤3

T(n) = 3000 + 900n for 4≤n≤6

T(n) = 1700n - 1800 for n>6