Doubling Question: how many after doubling 8 times?

[Joe Burton]

My daughter was asked the following question on a quiz yesterday. It is through a cyber school and the quiz has been graded. I have contacted the teacher regarding the answer, but wanted to get a second or several opinions. I have copy and pasted the question as it appeared in the lesson.

Thanks in advance

<Question text>

Doubling a grain of rice 8 times will you _____.
Select one:
a. 256 grains of rice
b. 8192 grains of rice
c. 128 grains of rice
d. 1024 grains of rice

</Question text>

 

[Deleted member 4993]

My daughter was asked the following question on a quiz yesterday. It is through a cyber school and the quiz has been graded. I have contacted the teacher regarding the answer, but wanted to get a second or several opinions. I have copy and pasted the question as it appeared in the lesson.

Thanks in advance,


Question text

[COLOR=rgba(0, 0, 0, 0.701961)]Doubling a grain of rice 8 times will you _____.
[/COLOR]
[COLOR=rgba(0, 0, 0, 0.701961)]Select one:
a. 256 grains of rice
b. 8192 grains of rice
c. 128 grains of rice
d. 1024 grains of rice

[/COLOR]

Question tex

Doubling once → 1* 2 = 2 = 2¹

Doubling twice → 2* 2¹ = 4 = 2²

Doubling three times → 2² * 2 = 8 = 2³

Doubling four times → 2³* 2 = 16 = 2⁴

Doubling five times → 2⁴* 2 = 32 = 2⁵

Doubling n times → 2^n-1* 2 = 2ⁿ

 

[stapel]

My daughter was asked the following question on a quiz yesterday.... the quiz has been graded. I have contacted the teacher regarding the answer, but wanted to get a second or several opinions....

Doubling a grain of rice 8 times will you _____.

Are you saying that you disagree with the instructor's answer? What was that answer? What was your daughter's answer?

Please be complete. Thank you!

 

[Joe Burton]

I apologize for not giving all the details. My daughter answered 256. I figured it out to be 256. The teacher insists the answer is 128, her explanation is in bold directly below.

"Yes -- on day 1 -- you start with 1 -- think of it as a loan -- you do not have to pay interest until Day 2 starts"

The question is: Doubling a grain of rice 8 times will you ________

Our Rationale:
We assumed we were starting with a grain of rice, one, therefore the first doubling would equal 2

1st = 2
2nd = 4
3rd = 8
4th = 16
5th = 32
6th = 64
7th = 128
8th = 256

Thanks again for the feedback.

 

[Joe Burton]

Thanks for the help Subhotosh Khan.

 

[ksdhart]

Based on what your daughter's teacher said, I believe that the question is worded very poorly. If the teacher wanted you to think in that way, it would need to be worded something like this:

"A wizard has one grain of rice. Every morning at sunrise, he casts a spell which doubles the number of grains of rice he has. After sunrise on the 8th day, how many grains of rice will the wizard have?"

Then you'd work it out and the teacher's reasoning could apply. The first doubling spell doesn't occur until the sunrise of day two. And thus on the 8th day's sunrise, the wizard will double his grains for the seventh time, so 2⁷ or 128 grains is the correct answer. However, that's not how this problem was worded. You're asked "[After] [d]oubling a grain of rice 8 times [you will have] ___" and no amount of hand-waving it in terms of loans and days and other such nonsense changes the fact that the way the teacher solves it, she's only doubling seven times, not eight.

 

[Joe Burton]

Thanks for the feedback ksdhart.

I agree 100% with your reasoning and explanation. The teacher was adamant about her answer (128) which had me second guessing my ability to solve the question. I needed a second opinion to bring me back from the ledge .

Thanks again for the help.

Also, thanks to the founder/creator of the board. It is/was a great idea and implementation.