Problem 2: Priya is walking down a long hallway. She walks halfway and stops. Then, she walks half of the remaining distance, and

stops again. She continues to stop every time she goes half of the remaining distance.

1. What fraction of the length of the hallway will Priya have covered after she starts and stops two times?

2. What fraction of the length of the hallway will Priya have covered after she starts and stops four times?

3. Will Priya ever reach the end of the hallway, repeatedly starting and stopping at half the remaining distance? Explain

your thinking.

The answers to the questions about problem 2 are:

Step-by-step explanation:

The explanation about each answer is below:

1. In the first stop, Priya has walked half of the total length, and there would still be half the hallway, however, when she stops the second time, she has walked the half of the half, I mean:

If you add the two values you obtain the total distance traveled by Priya:

And the distance traveled in two stops is 3/4 of the total length of the hallway.

2. With four stops the system is the same, we know with two stops Priya travels 3/4 of the hallway, now with the third stop, she will travel half of the remaining distance:

And in the fourth stop she will travel half of the remaining, I mean:

Now, we add all the values of the distances obtained:

So, the distance traveled by Priya in the fourth stop is 15/16 of the total length of the hallway.

3. How we know, the numbers are infinite, in the same forms the distances, by this reason, how the problem says that Priya walks just half of the distance, she will never reach the end because despite she has very near of the end, she will continue walking just half and ever smaller distances.

312312

step-by-step explanation:

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.