Question

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.

Answer 1

388,500 Dollars

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:

`sum = (t)/(2) (2s(1) + (t-1)d)`

where s(1) = 28800

t=30

d= -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