Problem: Bacterial cell divides every one minute. It takes 15 minutes a cup to be filled one-fourth. How much time will it take to fill the cup full?

Solution:
The problem involves two different time intervals: the time it takes for the bacterial cells to double and the time it takes for the cup to be filled. We can use exponential growth to solve this problem.

Step 1: Calculate the growth rate of bacterial cells

Since bacterial cells divide every one minute, the growth rate is 2. That means that the number of bacterial cells doubles every minute.

Step 2: Calculate the time it takes for the bacterial cells to fill the cup

We know that it takes 15 minutes for the cup to be filled one-fourth. That means that after 15 minutes, the cup has 25% of its capacity filled. Since the bacterial cells double every minute, we can calculate the number of bacterial cells after 15 minutes using the formula:

Nt = N0 x 2^t

where Nt is the number of bacterial cells after time t, N0 is the initial number of bacterial cells (1), and t is the time in minutes (15).

Nt = 1 x 2^15
Nt = 32,768

This means that after 15 minutes, there are 32,768 bacterial cells in the cup.

Step 3: Calculate the time it takes for the cup to be filled completely

Since the cup is one-fourth full after 15 minutes, we know that it will take 3 more intervals of bacterial cell growth to fill the cup completely. That means that the cup will be filled after 15 + 3 = 18 minutes.

Step 4: Answer the question

Therefore, the time it takes to fill the cup full is 18 minutes. The correct answer is (d) 17 minutes.

It take the time to full up the cup in 17 minutes because every one minutes it become double.. because bacteria is binary fission method..i.e.every one divison two new bacteria is produced...so which mean option "D" is correct..