Question

I have this homework question:

Assume a Database table has 0 records at time n=0. Suppose that at time n, 100n new records are populated into that table. The number of records increases 20 percent per minute. Write a recurrence relation and an initial condition that define the number of records in the database table. If each record in the database table consists of 50KB at what time n will the table have a size greater than 1GB?

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so from reading the question I know that:

F(0) = 0 at time 0 there are 0 records

The part that ticks me about this question is "Suppose that at time n, 100n new records are populated"

that will mean then:

F(1) = 100

F(2) = 200

F(3) = 300

If the problem will said suppose that at the first minute 100 new records where created then I will know that on the next minute 120 items will be created then 144 etc.. I believe my instructor formulated the question incorrectly.

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EDIT:

The actual question does not deals with database records I modify it in order to make it more appropiate to ask it in here. I been strugling to much with this homework. One of the reasons I believe is because the teacher types his own questions and he does not explain right what he means. this is the actual question:

Assume the deer population of Monroe County is 0 at time n = 0.
Suppose that at time n, 100n deer are introduced into Monroe County
and that the population increases 20 percent each year. Write a
recurrence relation and an initial condition that define the deer
population at time n and then solve the recurrence relation. (10
points).

and this is my answer so far:

Question says: Suppose that at time n, 100n deer are introduced into Monroe. In other words, the first year 100 deer are brought, the second year 200 deer are brought, the third 300 etc.. This could be interpreted with the recursive relation: T(n)=T(n-1)+100

Question also says that population increases 20 percent each year. This could be interpreted with the following recurrence relation: T(n)=T(n-1)*120%

Now we have to combine the recursive relations in order to get:

T(n)=T(n-1)*120%+100          where T(0)=0

I don’t know if that is right. I know the basics of recursion algorithms but I think the question could be asked in a different way making it easier to understand how exactly the population grows.

Answer 1

I think the situation is like this: at nth minute 100n new records are added, and the records stored upto (n – 1)th minute increases by 20%.

So, the recurrence should be:

F(0) = 0  <-- initial condition
F(n) = 1.2 * F(n - 1) + 100 * n where n > 0

A few steps explained:

 n  F(n)  Size(KB)
-- -----  --------
 0     0       0
 1   100    5000
 2   320   16000
 3   684   34200
 4  1220   61000
 5  1964   98200