A warehouse charges its customers 5 dollars per day for every 10 cubic feet for space used. Suppose the number of cubic feet a company uses on day t is given by s(t)=29000−200t. Find how much the company pays for 30 days.

Accepted Solution

Answer:388,500 Dollars Step-by-step explanation:This is a problem which can be solved by using sequences. The total number of days is 30. Let us say n=30 Now we see that for each day that passes by there is decrease in s by a quantity equal to 200 for example s(1) = 29000-200(1) = 28800& s(2) = 29000-200(2) = 28600 So difference between s(1) and s(2) = 200 let us call it d For such a decreasing arithmetic  sequence we can use the following formula to sum up all the spaced used over 30 days:[tex]sum = \frac{t}{2} (2s(1) + (t-1)d)[/tex]where s(1) = 28800t=30d= -200 (since it is decreasing) Putting the above in the equation we get Total space used = 777,000 Cubic Feet Price per 10 cubic feet = 5 Dollars Total Price = (777,000*5)/10 = 388,500 USD